Relevant bibliographies by topics / Dicolouring

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  1. Journal articles
  2. Dissertations / Theses

Academic literature on the topic 'Dicolouring'

Author: Grafiati
Published: 7 July 2024
Last updated: 31 July 2025

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Journal articles on the topic "Dicolouring"

1

Grinins, Juris, Guntis Sosins, Ilze Irbe, and Janis Zicans. "Weathering Resistance of Wood Following Thermal Modification in Closed Process Under Pressure in Nitrogen." Forests 16, no. 1 (2025): 132. https://doi.org/10.3390/f16010132.

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The wood of Scots pine (Pinus sylvestris), silver birch (Betula pendula), and European aspen (Populus tremula) was thermally modified in nitrogen under pressure. Three commercial linseed oil-based coatings without or with brown and grey pigments were applied to the specimens. Specimens were placed outside, and weathering stability was assessed for 3 months. The test measured total surface colour change (ΔE) and colonization by wood dicolouring fungi. Following the test, all uncoated specimens demonstrated poor colour fastness and resistance to fungal growth. All tested coatings were unsuitable
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2

Picasarri‐Arrieta, Lucas. "Strengthening the directed Brooks' theorem for oriented graphs and consequences on digraph redicolouring." Journal of Graph Theory, December 6, 2023. http://dx.doi.org/10.1002/jgt.23066.

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AbstractLet be a digraph. We define as the maximum of and as the maximum of . It is known that the dichromatic number of is at most . In this work, we prove that every digraph which has dichromatic number exactly must contain the directed join of and for some such that , except if in which case must contain a digon. In particular, every oriented graph with has dichromatic number at most . Let be an oriented graph of order such that . Given two 2‐dicolourings of , we show that we can transform one into the other in at most steps, by recolouring exactly one vertex at each step while maintaining
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3

Picasarri-Arrieta, Lucas. "Strengthening the Directed Brooks‘ Theorem for oriented graphs and consequences on digraph redicolouring." European Conference on Combinatorics, Graph Theory and Applications, no. 12 (August 28, 2023). http://dx.doi.org/10.5817/cz.muni.eurocomb23-105.

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Let $D=(V,A)$ be a digraph. We define $\Delta_{\max}(D)$ as the maximum of $\{ \max(d^+(v),d^-(v)) \mid v \in V \}$ and $\Delta_{\min}(D)$ as the maximum of $\{ \min(d^+(v),d^-(v)) \mid v \in V \}$. It is known that the dichromatic number of $D$ is at most $\Delta_{\min}(D) + 1$. In this work, we prove that every digraph $D$ which has dichromatic number exactly $\Delta_{\min}(D) + 1$ must contain the directed join of $\overleftrightarrow{K_r}$ and $\overleftrightarrow{K_s}$ for some $r,s$ such that $r+s = \Delta_{\min}(D) + 1$, except if $\Delta_{\min}(D) = 2$ in which case $D$ must contain a
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4

Aboulker, Pierre, and Quentin Vermande. "Various Bounds on the Minimum Number of Arcs in a $k$-Dicritical Digraph." Electronic Journal of Combinatorics 31, no. 1 (2024). http://dx.doi.org/10.37236/11549.

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The dichromatic number $\vec{\chi}(G)$ of a digraph $G$ is the least integer $k$ such that $G$ can be partitioned into $k$ acyclic digraphs. A digraph is $k$-dicritical if $\vec{\chi}(G) = k$ and each proper subgraph $H$ of $G$ satisfies $\vec{\chi}(H) \leq k-1$. 
 We prove various bounds on the minimum number of arcs in a $k$-dicritical digraph, a structural result on $k$-dicritical digraphs and a result on list-dicolouring. We characterise $3$-dicritical digraphs $G$ with $(k-1)|V(G)| + 1$ arcs. For $k \geq 4$, we characterise $k$-dicritical digraphs $G$ on at least $k+1$ vertices and w
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Dissertations / Theses on the topic "Dicolouring"

1

Picasarri-Arrieta, Lucas. "Coloration de graphes dirigés." Electronic Thesis or Diss., Université Côte d'Azur, 2024. http://www.theses.fr/2024COAZ4023.

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Cette thèse est dédiée à l'étude de la dicoloration, une notion de coloration pour les digraphes introduite par ErdH{o}s et Neumann-Lara à la fin des années 1970, ainsi que le paramètre qui lui est associé, à savoir le nombre dichromatique. Au cours des dernières décennies, ces deux notions ont permis de généraliser de nombreux résultats classiques de coloration de graphes. Nous commençons par donner différentes bornes sur le nombre dichromatique des digraphes dont le graphe sous-jacent est un graphe cordal. Ensuite, nous améliorons la borne donnée par le théorème de Brooks pour les digraphes
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