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- W1994856976 abstract "For a planar graph G, let $Delta(G)$, $g(G)$, and $lambda(G;p,q)$ denote, respectively, its maximum degree, girth, and $L(p,q)$-labeling number. We prove that (1) $lambda(G;p,q)le (2q-1)Delta(G)+4p+4q-4$ if $g(G)ge 7$; (2) $lambda(G;p,q)le (2q-1)Delta(G)+6p+12q-9$ if $g(G)ge 6$; (3) $lambda(G;p,q)le (2q-1)Delta(G)+6p+24q-15$ if $g(G)ge 5$. These bounds have consequences on conjectures by Wegner [Graphs with Given Diameter and a Coloring Problem, preprint, University of Dortmund, Dortmund, Germany, 1977] and Griggs and Yeh [SIAM J. Discrete Math., 5 (1992), pp. 586--595]." @default.
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- W1994856976 date "2003-01-01" @default.
- W1994856976 modified "2023-09-23" @default.
- W1994856976 title "Labeling Planar Graphs with Conditions on Girth and Distance Two" @default.
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- W1994856976 doi "https://doi.org/10.1137/s0895480101390448" @default.
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