List Total Weighting of Graphs
List Total Weighting of Graphs
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DOI：
10.1007/978-3-642-13580-4_13
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发表时间：
2010
影响因子：
15.1
通讯作者：
T. Wong;Xuding Zhu;Daqing Yang
中科院分区：
文献类型：
--
作者：
T. Wong;Xuding Zhu;Daqing Yang
A graphG=(V,E)is (k, k′)-total weight choosable if the following is true: For any (k, k′)-total list assignmentLthat assigns to each vertexva setL(v)ofkreal numbers as permissible weights, and assigns to each edgeea setL(e)ofk′real numbers as permissible weights, there is a proper L-total weighting, i.e., a mappingf:V∪E→ℝ such thatf(y)∈L(y) for eachy∈V∪E, and for any two adjacent verticesuandv, ∑e∈E(u)f(e)+f(u)≠∑e∈E(v)f(e)+f(v). This Paper introduces a method, the max-min weighting method, for finding proper L-total weightings of graphs. Using this method, we prove that complete multipartite graphs of the formKn,m,1,1,...,1are (2,2)-total weight choosable and complete bipartite graphs other thanK2are (1,2)-total weight choosable.
