Relevant bibliographies by topics / Odd colouring

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers

Academic literature on the topic 'Odd colouring'

Author: Grafiati
Published: 25 May 2024
Last updated: 31 July 2025

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Journal articles on the topic "Odd colouring"

1

KANG, ROSS J., and FRANÇOIS PIROT. "Distance Colouring Without One Cycle Length." Combinatorics, Probability and Computing 27, no. 5 (2018): 794–807. http://dx.doi.org/10.1017/s0963548318000068.

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We consider distance colourings in graphs of maximum degree at most d and how excluding one fixed cycle of length ℓ affects the number of colours required as d → ∞. For vertex-colouring and t ⩾ 1, if any two distinct vertices connected by a path of at most t edges are required to be coloured differently, then a reduction by a logarithmic (in d) factor against the trivial bound O(dt) can be obtained by excluding an odd cycle length ℓ ⩾ 3t if t is odd or by excluding an even cycle length ℓ ⩾ 2t + 2. For edge-colouring and t ⩾ 2, if any two distinct edges connected by a path of fewer than t edges
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ZELENYUK, YEVHEN, and YULIYA ZELENYUK. "COUNTING SYMMETRIC BRACELETS." Bulletin of the Australian Mathematical Society 89, no. 3 (2013): 431–36. http://dx.doi.org/10.1017/s0004972713000701.

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AbstractAn $r$-ary necklace (bracelet) of length $n$ is an equivalence class of $r$-colourings of vertices of a regular $n$-gon, taking all rotations (rotations and reflections) as equivalent. A necklace (bracelet) is symmetric if a corresponding colouring is invariant under some reflection. We show that the number of symmetric $r$-ary necklaces (bracelets) of length $n$ is $\frac{1}{2} (r+ 1){r}^{n/ 2} $ if $n$ is even, and ${r}^{(n+ 1)/ 2} $ if $n$ is odd.
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Kang, Dong Yeap, and Sang-Il Oum. "Improper colouring of graphs with no odd clique minor." Combinatorics, Probability and Computing 28, no. 5 (2019): 740–54. http://dx.doi.org/10.1017/s0963548318000548.

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AbstractAs a strengthening of Hadwiger’s conjecture, Gerards and Seymour conjectured that every graph with no oddKtminor is (t− 1)-colourable. We prove two weaker variants of this conjecture. Firstly, we show that for eacht⩾ 2, every graph with no oddKtminor has a partition of its vertex set into 6t− 9 setsV1, …,V6t−9such that eachViinduces a subgraph of bounded maximum degree. Secondly, we prove that for eacht⩾ 2, every graph with no odd Kt minor has a partition of its vertex set into 10t−13 setsV1,…,V10t−13such that eachViinduces a subgraph with components of bounded size. The second theorem
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KAWARABAYASHI, KEN-ICHI. "A Weakening of the Odd Hadwiger's Conjecture." Combinatorics, Probability and Computing 17, no. 6 (2008): 815–21. http://dx.doi.org/10.1017/s0963548308009462.

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Gerards and Seymour (see [10], p. 115) conjectured that if a graph has no odd complete minor of order l, then it is (l − 1)-colourable. This is an analogue of the well-known conjecture of Hadwiger, and in fact, this would immediately imply Hadwiger's conjecture. The current best-known bound for the chromatic number of graphs with no odd complete minor of order l is $O(l \sqrt{\log l})$ by the recent result by Geelen, Gerards, Reed, Seymour and Vetta [8], and by Kawarabayashi [12] later, independently. But it seems very hard to improve this bound since this would also improve the current best-k
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BOUSQUET, NICOLAS, LOUIS ESPERET, ARARAT HARUTYUNYAN, and RÉMI DE JOANNIS DE VERCLOS. "Exact Distance Colouring in Trees." Combinatorics, Probability and Computing 28, no. 2 (2018): 177–86. http://dx.doi.org/10.1017/s0963548318000378.

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For an integer q ⩾ 2 and an even integer d, consider the graph obtained from a large complete q-ary tree by connecting with an edge any two vertices at distance exactly d in the tree. This graph has clique number q + 1, and the purpose of this short note is to prove that its chromatic number is Θ((d log q)/log d). It was not known that the chromatic number of this graph grows with d. As a simple corollary of our result, we give a negative answer to a problem of van den Heuvel and Naserasr, asking whether there is a constant C such that for any odd integer d, any planar graph can be coloured wi
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Bryant, Darryn, and C. A. Rodger. "On the completion of latin rectangles to symmetric latin squares." Journal of the Australian Mathematical Society 76, no. 1 (2004): 109–24. http://dx.doi.org/10.1017/s1446788700008739.

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AbstractWe find necessary and sufficient conditions for completing an arbitrary 2 by n latin rectangle to an n by n symmetric latin square, for completing an arbitrary 2 by n latin rectangle to an n by n unipotent symmetric latin square, and for completing an arbitrary 1 by n latin rectangle to an n by n idempotent symmetric latin square. Equivalently, we prove necessary and sufficient conditions for the existence of an (n−1)-edge colouring of Kn (n even), and for n-edge colouring of Kn (n odd) in which the colours assigned to the edges incident with two vertices are specified in advance.
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D. Kavitha Thenmozhi. "Optimizing Balanced Networks with Strong Equitable Edge Colouring." Journal of Information Systems Engineering and Management 10, no. 8s (2025): 545–50. https://doi.org/10.52783/jisem.v10i8s.1110.

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Equitable edge colouring is a sophisticated network labelling technique with no more than one difference in the number of edges between any two colour groups. In this study, we applied the equitable edge-coloring technique to triangulated networks, utilizing the minimal number of edge colours, denoted by Δ. The structural characteristics of horse stride, branch flow, and tri-wing networks are presented in this research. The technique ensures optimized network performance, regardless of whether the triangular graphs involved are in even or odd quantities, reinforcing the robustness of this meth
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8

KINNERSLEY, WILLIAM B., KEVIN G. MILANS, and DOUGLAS B. WEST. "Degree Ramsey Numbers of Graphs." Combinatorics, Probability and Computing 21, no. 1-2 (2012): 229–53. http://dx.doi.org/10.1017/s0963548311000617.

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Let HG mean that every s-colouring of E(H) produces a monochromatic copy of G in some colour class. Let the s-colour degree Ramsey number of a graph G, written RΔ(G; s), be min{Δ(H): HG}. If T is a tree in which one vertex has degree at most k and all others have degree at most ⌈k/2⌉, then RΔ(T; s) = s(k − 1) + ϵ, where ϵ = 1 when k is odd and ϵ = 0 when k is even. For general trees, RΔ(T; s) ≤ 2s(Δ(T) − 1).To study sharpness of the upper bound, consider the double-starSa,b, the tree whose two non-leaf vertices have degrees a and b. If a ≤ b, then RΔ(Sa,b; 2) is 2b − 2 when a < b and b is e
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9

Stone, Phil. "Non-Mathematical Musings on Information Theory and Networked Musical Practice." Organised Sound 26, no. 3 (2021): 327–32. http://dx.doi.org/10.1017/s1355771821000418.

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Claude Shannon’s 1948 paper ‘A Mathematical Theory of Communication’ provided the essential foundation for the digital/information revolution that enables these very pixels to glow in meaningful patterns and permeates nearly every aspect of modern life. Information Theory, born fully grown from this paper, has been applied and mis-applied to a multitude of disciplines in the last 70-odd years, from quantum physics to psychology. Shannon himself famously decried those jumping on the ‘scientific bandwagon’ of Information Theory without sufficient mathematical rigour. Nevertheless, having a brief
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10

Jayawardene, C. J., J. N. Senadheera, K. A. S. N. Fernando, and W. C. W. Navaratna. "On Star-critical (K1,n, K1,m + e) Ramsey Numbers." Annals of Pure and Applied Mathematics 22, no. 02 (2020): 75–82. http://dx.doi.org/10.22457/apam.v22n2a02702.

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We say that Kn → (G,H), if for every red/blue colouring of edges of the complete graph Kn, there exists a red copy of G, or a blue copy of H in the colouring of Kn. The Ramsey number r(G,H) is the smallest positive integer n such that Kn → (G,H). Let r(n,m)=r(Kn, Km). A closely related concept of Ramsey numbers is the Star-critical Ramsey number r*(G, H) defined as the largest value of k such that K r(G,H)-1 ˅ K 1,k → (G,H). Literature on survey papers in this area reveals many unsolved problems related to these numbers. One of these problems is the calculation of Ramsey numbers for certain cl
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Dissertations / Theses on the topic "Odd colouring"

1

Ouyang, Qiancheng. "Some colouring problems in edge/vertex-coloured graphs : Structural and extremal studies." Electronic Thesis or Diss., université Paris-Saclay, 2023. http://www.theses.fr/2023UPASG060.

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La coloration de graphes est l'un des sujets les plus connus, populaires et largement étudiés dans le domaine de la théorie des graphes, avec une vaste littérature comprenant des approches provenant de nombreux domaines ainsi que de nombreux problèmes qui sont encore ouverts et étudiés par divers mathématiciens et informaticiens à travers le monde. Le Problème des Quatre Couleurs, à l'origine de l'étude de la coloration des graphes, a été l'un des problèmes centraux en théorie des graphes au siècle dernier. Il demande s'il est possible de colorer proprement chaque graphe planaire avec quatre c
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Books on the topic "Odd colouring"

1

Fairly Coloring Book: Funny Unofficial Odd Collection Parents a an Adult Colouring Books Exclusive Illustrations. Independently Published, 2022.

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2

Barnes, Jaxson. Odd Squad Waves Diagonals Lines Swirls Dots Coloring Book: Awesome Illustrations Spirograph Styles Colouring Books for Adult. Independently Published, 2021.

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Barnes, Jaxson. Odd Squad Waves Diagonals Lines Swirls Dots Coloring Book: Premium Spirograph Styles Colouring Books for Adult and Kid! Independently Published, 2021.

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4

Publishing, Skellee. Colouring and Brain Teaser Activities for Kids Ages 6-8 8-10 UK Version - Secret Codes - I Spy - Sudoku - Mazes - Odd One Out - Word Search - Scramble: An Activity Book Packed with over 100 Puzzles. Independently Published, 2020.

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Book chapters on the topic "Odd colouring"

1

Hickingbotham, Robert, Dong Yeap Kang, Sang-il Oum, Raphael Steiner, and David R. Wood. "Clustered Colouring of Odd-H-Minor-Free Graphs." In MATRIX Book Series. Springer Nature Switzerland, 2025. https://doi.org/10.1007/978-3-031-76738-8_4.

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"colouring | coloring, adj." In Oxford English Dictionary, 3rd ed. Oxford University Press, 2023. http://dx.doi.org/10.1093/oed/1128518023.

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"colouring | coloring, n." In Oxford English Dictionary, 3rd ed. Oxford University Press, 2023. http://dx.doi.org/10.1093/oed/4746329854.

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"dead-colouring | dead-coloring, n." In Oxford English Dictionary, 3rd ed. Oxford University Press, 2024. http://dx.doi.org/10.1093/oed/1170837837.

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"colouring in | coloring in, n." In Oxford English Dictionary, 3rd ed. Oxford University Press, 2023. http://dx.doi.org/10.1093/oed/8578639611.

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"colouring matter | coloring matter, n." In Oxford English Dictionary, 3rd ed. Oxford University Press, 2023. http://dx.doi.org/10.1093/oed/7325500347.

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Krishnamurti, Bhadriraju, and Murray B. Emeneau. "Evidence for a Laryngeal *H in Proto-Dravidian." In Comparative Dravidian Linguistics. Oxford University PressOxford, 2001. http://dx.doi.org/10.1093/oso/9780198241225.003.0019.

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"colourish, n." In Oxford English Dictionary, 3rd ed. Oxford University Press, 2023. http://dx.doi.org/10.1093/oed/7103047581.

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"colourize | colorize, v." In Oxford English Dictionary, 3rd ed. Oxford University Press, 2023. http://dx.doi.org/10.1093/oed/6429298936.

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"colourist | colorist, n." In Oxford English Dictionary, 3rd ed. Oxford University Press, 2023. http://dx.doi.org/10.1093/oed/4842462689.

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Conference papers on the topic "Odd colouring"

1

Bernardi, João Pedro W., Sheila M. De Almeida, and Leandro M. Zatesko. "On Total and Edge-colouring of Proper Circular-arc Graphs." In III Encontro de Teoria da Computação. Sociedade Brasileira de Computação - SBC, 2018. http://dx.doi.org/10.5753/etc.2018.3557.

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Deciding if a graph is Δ-edge-colourable (resp. (Δ + 1)-total colourable), although it is an NP-complete problem for graphs in general, is polynomially solvable for interval graphs of odd (resp. even) maximum degree Δ. An interesting superclass of the proper interval graphs are the proper circular-arc graphs, for which we suspect that Δ-edge-colourability is linear-time decidable. This work presents sufficient conditions for Δ-edge-colourability, (Δ + 1)-total colourability, and (Δ+2)-total colourability of proper circular-arc graphs. Our proofs are constructive and yield polynomial-time algor
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