Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5776853 | Discrete Mathematics | 2017 | 10 Pages |
Abstract
A total weighting of a graph G is a function Ï that assigns a weight to each vertex and each edge of G. The vertex-sum of a vertex v with respect to Ï is SÏ(v)=Ï(v)+âeâE(v)Ï(e), where E(v) is the set of edges incident to v. A total weighting is proper if adjacent vertices have distinct vertex-sums. A graph G is (k,kâ²)-choosable if the following is true: Whenever each vertex x is assigned a set L(x) of k real numbers and each edge e is assigned a set L(e) of kâ² real numbers, there is a proper total weighting Ï of G with Ï(y)âL(y) for all yâV(G)âªE(G). In this paper, we prove that for pâ{5,7,11}, a graph G without isolated edges and with mad(G)â¤pâ1 is (1,p)-choosable. In particular, triangle-free planar graphs are (1,5)-choosable.
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
Authors
Yunfang Tang, Xuding Zhu,