L(p,q)-labeling of sparse graphs

Clément Charpentier (), Mickaël Montassier () and André Raspaud ()
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Clément Charpentier: Université de Bordeaux
Mickaël Montassier: Université de Bordeaux
André Raspaud: Université de Bordeaux

Journal of Combinatorial Optimization, 2013, vol. 25, issue 4, No 13, 646-660

Abstract: Abstract Let p and q be positive integers. An L(p,q)-labeling of a graph G with a span s is a labeling of its vertices by integers between 0 and s such that adjacent vertices of G are labeled using colors at least p apart, and vertices having a common neighbor are labeled using colors at least q apart. We denote by λ p,q (G) the least integer k such that G has an L(p,q)-labeling with span k. The maximum average degree of a graph G, denoted by $\operatorname {Mad}(G)$ , is the maximum among the average degrees of its subgraphs (i.e. $\operatorname {Mad}(G) = \max\{\frac{2|E(H)|}{|V(H)|} ; H \subseteq G \}$ ). We consider graphs G with $\operatorname {Mad}(G) p. λ p,q (G)≤(2q−1)Δ+4p+6q−5 if m

Keywords: Graph theory; Graph labeling; Graph coloring; Sparse graphs (search for similar items in EconPapers)
Date: 2013
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DOI: 10.1007/s10878-012-9507-6

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