NDLI: Construction of Large Graphs with No Optimal Surjective L(2,1)-Labelings

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Skrekovski, Riste Krl', Daniel Tancer, Martin
Copyright Year	2006
Abstract	An L(2,1)-labeling of a graph G is a mapping c : V(G) \to {0,...,K} such that the labels of two adjacent vertices differ by at least two and the labels of vertices at distance two differ by at least one. A hole of c is an integer h \in {0,...,K} that is not used as a label for any vertex of G. The smallest integer K for which an L(2,1)-labeling of G exists is denoted by lambda(G). The minimum number of holes in an optimal labeling, i.e., a labeling with K = lambda(G), is denoted by rho(G). Georges and Mauro [SIAM J. Discrete Math., 19 (2005), pp. 208-223] showed that rho(G) \le Delta, where Delta is the maximum degree of G, and conjectured that if rho(G) = Delta and G is connected, then the order of G is at most Delta(Delta + 1). We disprove this conjecture by constructing graphs G with rho(G) = Delta and order \lfloor (Delta + 1)2/4 \rfloor (Delta + 1) \approx Delta3 /4.
Starting Page	536
Ending Page	543
Page Count	8
File Format	PDF
ISSN	08954801
DOI	10.1137/050623061
e-ISSN	10957146
Journal	SIAM Journal on Discrete Mathematics (SJDMEC)
Issue Number	2
Volume Number	20
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2006-08-01
Access Restriction	Subscribed
Subject Keyword	graph labeling with distance conditions Coloring of graphs and hypergraphs channel assignment problem
Content Type	Text
Resource Type	Article
Subject	Mathematics

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