An adjacent vertex distinguishing edge-coloring of a graph G is a proper edge-coloring o G such that any pair of adjacent vertices are incident to distinct sets of colors. The minimum number of colors required for an adjacent vertex distinguishing edge-coloring of G is denoted by χ'ₐ(G). We prove that χ'ₐ(G) is at most the maximum degree plus 2 if G is a planar graph without isolated edges whose girth is at least 6. This gives new evidence to a conjecture proposed in [Z. Zhang, L. Liu, and J. Wang, Adjacent strong edge coloring of graphs, Appl. Math. Lett., 15 (2002) 623-626.]
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1556,
author = {Yuehua Bu and Ko-Wei Lih and Weifan Wang},
title = {Adjacent vertex distinguishing edge-colorings of planar graphs with girth at least six},
journal = {Discussiones Mathematicae Graph Theory},
volume = {31},
year = {2011},
pages = {429-439},
zbl = {1229.05100},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1556}
}
Yuehua Bu; Ko-Wei Lih; Weifan Wang. Adjacent vertex distinguishing edge-colorings of planar graphs with girth at least six. Discussiones Mathematicae Graph Theory, Tome 31 (2011) pp. 429-439. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1556/
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