DMTCS Proceedings, 2005 European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05)

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DMTCS Conference vol AE (2005), pp. 41-44

DMTCS

2005 European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05)

Stefan Felsner (ed.)

DMTCS Conference Volume AE (2005), pp. 41-44


author: Peter Bella, Daniel Král', Bojan Mohar and Katarína Quittnerová
title: Labeling planar graphs with a condition at distance two
keywords:
L(2,1)
-labeling, channel assignment problem, graph coloring, planar graphs
abstract: An
L(2,1)
-labeling of a graph is a mapping
c:V(G)→{0,…,K}
such that the labels assigned to neighboring vertices differ by at least
2
and the labels of vertices at distance two are different. Griggs and Yeh [SIAM J. Discrete Math. 5 (1992), 586--595] conjectured that every graph
G
with maximum degree
Δ
has an
L(2,1)
-labeling with
K≤Δ
2
. We verify the conjecture for planar graphs with maximum degree
Δ≠3
.
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reference: Peter Bella and Daniel Král' and Bojan Mohar and Katarína Quittnerová (2005), Labeling planar graphs with a condition at distance two , in 2005 European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05), Stefan Felsner (ed.), Discrete Mathematics and Theoretical Computer Science Proceedings AE, pp. 41-44
bibtex: For a corresponding BibTeX entry, please consider our BibTeX-file.
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