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Showing 1 to 3 of 3 for “"List Chromatic Number"”.
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Extremal problems on variations of graph colorings
… We produce a result of this type for the list chromatic number; namely, we prove that given a graph $G$ with maximum degree at least $10^{20}$, if $G$ has no clique of size $\Delta(G)$, then $G$ is $(\Delta(G)-1)$-choosable. Cai, Wang, and Zhu proved that a toroidal graph with no 6-cycles …
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The Chromatic Structure of Dense Graphs
… macroscopic structure. We primarily consider the chromatic structure: whether a graph has or is close to having some (low) chromatic number. Chapter 2 is the slight exception. We consider an induced version of the classical Turán problem. Introduced by Loh, Tait, Timmons, and Zhou, the induced …
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Extremal problems in graph theory
… of small radius and find the domination number of the Kneser graph $K(n,k)$ when $n\ge{3\over4}k\sp2\pm k,$ depending on whether k is even or odd. The path chromatic number $\chi\sb{P}(G)$ of a graph G is the least number of colors with which the vertices of G can be colored so that each …