On the L(h,k)-Labeling of Co-comparability Graphs View Full Text


Ontology type: schema:Chapter     


Chapter Info

DATE

2007

AUTHORS

Tiziana Calamoneri , Saverio Caminiti , Stephan Olariu , Rossella Petreschi

ABSTRACT

Given two non negative integers h and k, an L(h,k)-labeling of a graph G = (V,E) is a map from V to a set of labels such that adjacent vertices receive labels at least h apart, while vertices at distance at most 2 receive labels at least k apart. The goal of the L(h,k)-labeling problem is to produce a legal labeling that minimizes the largest label used. Since the decision version of the L(h,k)-labeling problem is NP-complete, it is important to investigate classes of graphs for which the problem can be solved efficiently. Along this line of though, in this paper we deal with co-comparability graphs and two of its subclasses: interval graphs and unit-interval graphs. Specifically, we provide, in a constructive way, the first upper bounds on the L(h,k)-number of co-comparability graphs and interval graphs. To the best of our knowledge, ours is the first reported result concerning the L(h,k)-labeling of co-comparability graphs. In the special case where k = 1, our result improves on the best previously-known approximation ratio for interval graphs. More... »

PAGES

116-127

Book

TITLE

Combinatorics, Algorithms, Probabilistic and Experimental Methodologies

ISBN

978-3-540-74449-8
978-3-540-74450-4

Author Affiliations

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/978-3-540-74450-4_11

DOI

http://dx.doi.org/10.1007/978-3-540-74450-4_11

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1014645727


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