AJOU Central Library Repository: 3차 정규그래프의 인접 리스트 채색에 관한 연구

Graduate School of Ajou University Department of Mathematics 3. Theses(Master)

3차 정규그래프의 인접 리스트 채색에 관한 연구

Alternative Abstract: 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.

Appears in Collections:: Graduate School of Ajou University > Department of Mathematics > 3. Theses(Master)

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