On the Hardness of Approximating the Chromatic Number

Following [1], we investigate the problem of covering a graph G with induced subgraphs G1,…, Gk of possibly smaller chromatic number, but such that for every vertex u of G, the sum of reciprocals of the chromatic numbers of the Gi's containing u is at least 1. The existence of such “chromatic coverings” provides some bounds on the chromatic number of G. © 2005 Wiley Periodicals, Inc.

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10.1002/jgt.20127

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Chromatic completion number

Journal of Mathematical and Computational Science (2020)

The well known concept of proper vertex colouring of a graph is used to introduce the construction of a chromatic completion graph and determining its related parameter, the chromatic completion number of a graph. The chromatic completion numbers of certain classes of cycle derivative graphs and helm graphs are then presented. Finally, we discuss further problems for research related to this concept.

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10.28919/jmcs/5028

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New Game Chromatic and Game Chromatic Number

Journal of China University of Mining and Technology (2000)

Ning We

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Source

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Bounds on the Dynamic Chromatic Number of a Graph in Terms of its Chromatic Number

Journal of Mathematical Sciences (2018)

N.Yu. Vlasova D. V. Karpov

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10.1007/s10958-018-3855-4

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Circular chromatic number

Discrete Mathematics (2001)

Xuding Zhu

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10.1016/s0012-365x(00)00217-x

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The fractional chromatic number of infinite graphs

Journal of Graph Theory (1995)

Imre Leader

Abstract The fractional chromatic number of a graph G is the infimum of the total weight that can be assigned to the independent sets of G in such a way that, for each vertex v of G , the sum of the weights of the independent sets containing v is at least 1. In this note we give a graph a graph whose fractional chromatic number is strictly greater than the supremum of the fractional chromatic numbers of its finite subgraphs. This answers a question of Zhu. We also give some grphs for which the fractional chromatic number is not attined, answering another of Zhu. © 1995 John Wiley & Sons, Inc.

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10.1002/jgt.3190200404

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On the Chromatic Number of $$\mathbb {R}^4$$ R 4

Discrete & Computational Geometry (2014)

Geoffrey Exoo Dan Ismailescu Michael Lim

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