Distance constrained labelings of planar graphs with no short cycles

Authors:
Zdenk Dvořák;Daniel Král';Pavel Nejedlý;Riste Škrekovski
Affiliations:
Department of Applied Mathematics, Faculty of Mathematics and Physics, Charles University, Malostranské námstí 25, 118 00 Prague, Czech Republic and Institute for Theoretical Comput ...;Institute for Theoretical Computer Science, Faculty of Mathematics and Physics, Charles University, Malostranské námstí 25, 118 00 Prague, Czech Republic11The Institute for Theoreti ...;Department of Applied Mathematics, Faculty of Mathematics and Physics, Charles University, Malostranské námstí 25, 118 00 Prague, Czech Republic;Department of Mathematics, University of Ljubljana, Jadranska 19, 1111 Ljubljana, Slovenia
Venue:
Discrete Applied Mathematics
Year:
2009

Citing 16
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Abstract

Motivated by a conjecture of Wang and Lih, we show that every planar graph of girth at least seven and maximum degree @D=190+2@?p/q@? has an L(p,q)-labeling of span at most 2p+q@D-2. Since the optimal span of an L(p,1)-labeling of an infinite @D-regular tree is 2p+@D-2, the obtained bound is the best possible for any p=1 and q=1.