淡江大學機構典藏:Item 987654321/115409
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    Please use this identifier to cite or link to this item: http://tkuir.lib.tku.edu.tw:8080/dspace/handle/987654321/115409


    Title: Parity and strong parity edge-colorings of graphs
    Authors: Hsiang-Chun Hsu;Gerard Jennhwa Chang
    Keywords: (Strong) parity edge-coloring;(Strong) parity edge-chromatic number;Hypercube embedding;Hopt-Stiefel function;Product of graphs
    Date: 2012-11-30
    Issue Date: 2018-10-25 12:11:04 (UTC+8)
    Publisher: Springer US
    Abstract: A parity walk in an edge-coloring of a graph is a walk along which each color is used an even number of times. A parity edge-coloring (respectively, strong parity edge-coloring) is an edge-coloring in which there is no nontrivial parity path (respectively, open parity walk). The parity edge-chromatic number p(G) (respectively, strong parity edge-chromatic number pˆ(G) ) is the least number of colors in a parity edge-coloring (respectively, strong parity edge-coloring) of G. Notice that pˆ(G)≥p(G)≥χ′(G)≥Δ(G) for any graph G. In this paper, we determine pˆ(G) and p(G) for some complete bipartite graphs and some products of graphs. For instance, we determine pˆ(Km,n) and p(K m,n ) for m≤n with n≡0,−1,−2 (mod 2⌈lg m⌉).
    Relation: Journal of Combinatorial Optimization 24(4), p.427-436
    DOI: 10.1007/s10878-011-9398-y
    Appears in Collections:[Graduate Institute & Department of Mathematics] Journal Article

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