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    題名: Max-coloring of vertex-weighted graphs
    作者: Hsiang-Chun Hsu;Gerard Jennhwa Chang
    關鍵詞: Coloring;Weighted graph;Perfection
    日期: 2016
    上傳時間: 2018-10-25 12:10:59 (UTC+8)
    出版者: Springer Japan
    摘要: A proper vertex coloring of a graph G is a partition \{A_1,A_2,\ldots ,A_k\} of the vertex set V(G) into stable sets. For a graph G with a positive vertex-weight c:V(G) \rightarrow (0,\infty ), denoted by (G,c), let \chi (G,c) be the minimum value of \sum _{i=1}^k \max _{v \in A_i} c(v) over all proper vertex coloring \{A_1,A_2,\ldots ,A_k\} of G and \sharp \chi (G,c) the minimum value of k for a proper vertex coloring \{A_1,A_2,\ldots ,A_k\} of G such that \sum _{i=1}^k \max _{v \in A_i} c(v) = \chi (G,c). This paper establishes an upper bound on \sharp \chi (G,c) for a weighted r-colorable graph (G,c), and a Nordhaus–Gaddum type inequality for \chi (G,c). It also studies the c-perfection for a weighted graph (G,c).
    關聯: Graphs and Combinatorics 32(1), p.191-198
    DOI: 10.1007/s00373-015-1562-1
    顯示於類別:[數學學系暨研究所] 期刊論文

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