随机图的包含色度指数

IF 0.9 3区数学 Q2 MATHEMATICS

Journal of Graph Theory Pub Date : 2024-02-14 DOI:10.1002/jgt.23088

Jakub Kwaśny, Jakub Przybyło

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引用次数: 0

摘要

Erdős 和 Wilson 于 1977 年证明，几乎所有图形的色度指数都等于其最大度数。2001 年，Balister 扩展了这一结果，并证明如果我们额外要求任意两个顶点的颜色集是不同的，那么相同数量的颜色几乎总是足够的。我们研究了一个更强的条件，并证明如果禁止任何一对相邻顶点包含这些颜色集，那么多一种颜色几乎总是充分且必要的。我们还确定了一个几乎适用于所有图形的限制性更强的图形不变式的价值，即禁止包含所有顶点对，这就要求偶数阶图形多一种颜色。

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Inclusion chromatic index of random graphs

Erdős and Wilson proved in 1977 that almost all graphs have chromatic index equal to their maximum degree. In 2001 Balister extended this result and proved that the same number of colours is almost always sufficient if we additionally demand the distinctness of the sets of colours incident with any two vertices. We study a stronger condition and show that one more colour is almost always sufficient and necessary if the inclusion of these sets is forbidden for any pair of adjacent vertices. We also settle the value of a more restrictive graph invariant for almost all graphs, where inclusion is forbidden for all pairs of vertices, which necessitates one more colour for graphs of even order.

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来源期刊

Journal of Graph Theory 数学-数学

CiteScore

1.60

自引率

22.20%

发文量

130

审稿时长

6-12 weeks

期刊介绍： The Journal of Graph Theory is devoted to a variety of topics in graph theory, such as structural results about graphs, graph algorithms with theoretical emphasis, and discrete optimization on graphs. The scope of the journal also includes related areas in combinatorics and the interaction of graph theory with other mathematical sciences. A subscription to the Journal of Graph Theory includes a subscription to the Journal of Combinatorial Designs .