Journal of Combinatorial Theory Series B ( IF 1.4 ) Pub Date : 2021-02-03 , DOI: 10.1016/j.jctb.2021.01.008 Lu Cao
Let be a graph. A proper total weighting of G is a mapping such that the following sum for each gives a proper vertex colouring of G. For any , we say that G is total weight -choosable if for any and , there exists a proper total weighting w of G such that for and for . A strengthening of the 1-2-3 Conjecture states that every graph without an isolated edge is total weight -choosable. In this paper, we prove that every graph without an isolated edge is total weight -choosable. We also prove some new results on the total weight choosability of bipartite graphs.
中文翻译:
图的总重量选择率:朝向1-2-3-猜想
让 成为图。G的适当总权重是一个映射 这样每个的以下总和 给出G的适当顶点着色。对于任何,我们说G是总重量-如果有的话可以选择 和 中,存在一个适当的总加权瓦特的ģ使得 对于 和 对于 。1-2-3猜想的增强表明,每个没有孤立边的图都是总权重-可选择。在本文中,我们证明了每个没有孤立边的图都是总权重-可选择。我们还证明了二部图的总权重选择性的一些新结果。