Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8902842 | Discrete Mathematics | 2018 | 6 Pages |
Abstract
A proper total weighting of a graph G is a mapping Ï which assigns to each vertex and each edge of G a real number as its weight so that for any edge uv of G, âeâE(v)Ï(e)+Ï(v)â âeâE(u)Ï(e)+Ï(u). A (k,kâ²)-list assignment of G is a mapping L which assigns to each vertex v a set L(v) of k permissible weights and to each edge e a set L(e) of kâ² permissible weights. An L-total weighting is a total weighting Ï with Ï(z)âL(z) for each zâV(G)âªE(G). A graph G is called (k,kâ²)-choosable if for every (k,kâ²)-list assignment L of G, there exists a proper L-total weighting. It was proved in Tang and Zhu (2017) that if pâ{5,7,11}, a graph G without isolated edges and with mad(G)â¤pâ1 is (1,p)-choosable. In this paper, we strengthen this result by showing that for any prime p, a graph G without isolated edges and with mad(G)â¤pâ1 is (1,p)-choosable.
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
Authors
Yu-Chang Liang, Yunfang Tang, Tsai-Lien Wong, Xuding Zhu,