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3차 정규그래프의 인접 리스트 채색에 관한 연구

초록/요약

An incidence of a graph G is a pair (u; e) where u is a vertex of G and e is an edge of G incident with u. Two incidences (u; e) and (v; f) of G are adjacent whenever (i) u = v, or (ii) e = f, or (iii) uv = e or uv = f. An incidence k-coloring of G is a mapping from the set of incidences of G to a set of k colors such that every two adjacent incidences receive distinct colors. The notion of incidence coloring has been introduced by Brualdi and Quinn Massey (1993) from a relation to strong edge coloring, and since then, attracted by many authors. On a list version of incidence coloring, it was shown by Benmedjdoub et. al. (2017) that every Hamiltonian cubic graph is incidence 6-choosable. In this paper, we show that every cubic (loopless) multigraph is incidence 6- choosable. As a direct consequence, it implies that the list strong chromatic index of a (2; 3)-bipartite graph is at most 6, where a (2,3)-bipartite graph is a bipartite graph such that one partite set has maximum degree at most 2 and the other partite set has maximum degree at most 3.

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목차

Contents
Abstract i
1 Introduction 1
1.1 Basic definitions in Graph Thoery . . . . . . . . . . . . . . . 1
1.2 Incidence coloring of a grpah . . . . . . . . . . . . . . . . . . 3
1.2.1 Definitions and Strong edge coloring . . . . . . . . . 3
1.2.2 Relation to other coloring notion . . . . . . . . . . . 5
1.3 Some known results . . . . . . . . . . . . . . . . . . . . . . . 6
1.4 Incidence choosability and the topics of the thesis . . . . . . 8
1.4.1 Incidence choosability . . . . . . . . . . . . . . . . . 8
1.4.2 Main theorem of the thesis . . . . . . . . . . . . . . 10
2 Main result 11
2.1 Outline of the proof of Theorem ?? . . . . . . . . . . . . . . 11
2.2 Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.3 Proofs of Theorems 2.1 and 2.2 . . . . . . . . . . . . . . . . 16
3 Concluding Remarks 25
국문초록 30

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