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Relevant bibliographies by topics / Chromatic Polynomials

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Journal articles

Academic literature on the topic 'Chromatic Polynomials'

Author: Grafiati

Published: 4 June 2021

Last updated: 6 February 2022

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Journal articles on the topic "Chromatic Polynomials"

1

Morgan, Kerri. "Galois groups of chromatic polynomials." LMS Journal of Computation and Mathematics 15 (September 1, 2012): 281–307. http://dx.doi.org/10.1112/s1461157012001052.

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AbstractThe chromatic polynomialP(G,λ) gives the number of ways a graphGcan be properly coloured in at mostλcolours. This polynomial has been extensively studied in both combinatorics and statistical physics, but there has been little work on its algebraic properties. This paper reports a systematic study of the Galois groups of chromatic polynomials. We give a summary of the Galois groups of all chromatic polynomials of strongly non-clique-separable graphs of order at most 10 and all chromatic polynomials of non-clique-separableθ-graphs of order at most 19. Most of these chromatic polynomials

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2

Wakelin, C. D. "Chromatic polynomials and ?-polynomials." Journal of Graph Theory 22, no. 4 (1996): 367–81. http://dx.doi.org/10.1002/(sici)1097-0118(199608)22:4<367::aid-jgt10>3.0.co;2-c.

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3

BIGGS, NORMAN. "CHROMATIC POLYNOMIALS FOR TWISTED BRACELETS." Bulletin of the London Mathematical Society 34, no. 2 (2002): 129–39. http://dx.doi.org/10.1112/s0024609301008931.

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This paper is concerned with the chromatic polynomials of ‘bracelets’: specifically, graphs constructed by taking n copies of a complete graph and linking them together in a ring. Using a sieve method, explicit formulae for the dominant and subdominant terms of the chromatic polynomial are obtained. Finally, a simple description of the effect of twisting the links is obtained.

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4

Robertson, Ian. "T-chromatic polynomials." Discrete Mathematics 135, no. 1-3 (1994): 279–86. http://dx.doi.org/10.1016/0012-365x(93)e0089-m.

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5

Ray, Nigel, and William Schmitt. "Ultimate chromatic polynomials." Discrete Mathematics 125, no. 1-3 (1994): 329–41. http://dx.doi.org/10.1016/0012-365x(94)90174-0.

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6

Rao, R. V. N. S., and J. V. Rao. "Classification of Algebraic Properties of Chromatic Polynomials." Journal of Scientific Research 5, no. 3 (2013): 469–77. http://dx.doi.org/10.3329/jsr.v5i3.11634.

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This manuscript attempts to introduce the concept of chromatic polynomials of total graphs using Mobius inversion theorem. In fact it studies various algebraic properties of chromatic polynomial using Mobius inversion theorem. Keywords: Bond lattice; Chromatic polynomial; Mobius function; Poset. © 2013 JSR Publications. ISSN: 2070-0237 (Print); 2070-0245 (Online). All rights reserved. doi: http://dx.doi.org/10.3329/jsr.v5i3.11634 J. Sci. Res. 5 (3), 469-477 (2013)

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7

Farrell, E. J., and Earl Glen Whitehead. "Connections between the matching and chromatic polynomials." International Journal of Mathematics and Mathematical Sciences 15, no. 4 (1992): 757–66. http://dx.doi.org/10.1155/s016117129200098x.

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The main results established are (i) a connection between the matching and chromatic polynomials and (ii) a formula for the matching polynomial of a general complement of a subgraph of a graph. Some deductions on matching and chromatic equivalence and uniqueness are made.

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8

Levin, Alexander B. "On the set of Hilbert polynomials." Bulletin of the Australian Mathematical Society 64, no. 2 (2001): 291–305. http://dx.doi.org/10.1017/s0004972700039952.

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We characterise the set of all Hilbert polynomials of standard graded algebras over a field and give solutions of some open problems on Hilbert polynomials. In particular, we prove that a chromatic polynomial of a graph is a Hilbert polynomial of some standard graded algebra.

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9

Kishore, Anjaly, and M. S. Sunitha. "On injective chromatic polynomials of graphs." Discrete Mathematics, Algorithms and Applications 07, no. 03 (2015): 1550035. http://dx.doi.org/10.1142/s1793830915500354.

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The injective chromatic number χi(G) [G. Hahn, J. Kratochvil, J. Siran and D. Sotteau, On the injective chromatic number of graphs, Discrete Math. 256(1–2) (2002) 179–192] of a graph G is the minimum number of colors needed to color the vertices of G such that two vertices with a common neighbor are assigned distinct colors. The nature of the coefficients of injective chromatic polynomials of complete graphs, wheel graphs and cycles is studied. Injective chromatic polynomial on operations like union, join, product and corona of graphs is obtained.

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10

Borowiecki, Mieczysław, and Ewa Łazuka. "Chromatic polynomials of hypergraphs." Discussiones Mathematicae Graph Theory 20, no. 2 (2000): 293. http://dx.doi.org/10.7151/dmgt.1128.

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