منابع مشابه
Total choosability of multicircuits I
A multicircuit is a multigraph whose underlying simple graph is a circuit (a connected 2-regular graph). In this pair of papers, it is proved that every multicircuit C has total choosability (i.e., list total chromatic number) ch00(C ) equal to its ordinary total chromatic number 00(C ). In the present paper, the kernel method is used to prove this for every multicircuit that
متن کاملTotal choosability of multicircuits II
A multicircuit is a multigraph whose underlying simple graph is a circuit (a connected 2-regular graph). In this paper, the method of Alon and Tarsi is used to prove that all multicircuits of even order, and some regular and near-regular multicircuits of odd order have total choosability (i.e., list total chromatic number) equal to their ordinary total chromatic number. This completes the proof...
متن کاملEdge-choosability of multicircuits
A multicircuit is a multigraph whose underlying simple graph is a circuit (a connected 2-regular graph). The List-Colouring Conjecture (LCC) is that every multigraph G has edgechoosability (list chromatic index) ch’(G) equal to its chromatic index x’(G). In this paper the LCC is proved first for multicircuits, and then, building on results of Peterson and Woodall, for any multigraph G in which ...
متن کاملChoosability conjectures and multicircuits
This paper starts with a discussion of several old and new conjectures about choosability in graphs. In particular, the list-colouring conjecture, that ch′ = ′ for every multigraph, is shown to imply that if a line graph is (a : b)-choosable, then it is (ta : tb)-choosable for every positive integer t. It is proved that ch(H )= (H ) for many “small” graphs H , including in9ations of all circuit...
متن کاملChoosability, Edge Choosability, and Total Choosability of Outerplane Graphs
Let χl (G), χ ′ l (G), χ ′′ l (G), and 1(G) denote, respectively, the list chromatic number, the list chromatic index, the list total chromatic number, and the maximum degree of a non-trivial connected outerplane graph G. We prove the following results. (1) 2 ≤ χl (G) ≤ 3 and χl (G) = 2 if and only if G is bipartite with at most one cycle. (2) 1(G) ≤ χ ′ l (G) ≤ 1(G) + 1 and χ ′ l (G) = 1(G) + ...
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ژورنال
عنوان ژورنال: Journal of Graph Theory
سال: 2002
ISSN: 0364-9024,1097-0118
DOI: 10.1002/jgt.10029