Coloring problem of signed interval graphs
Publish place: Transactions on Combinatorics، Vol: 8، Issue: 4
Publish Year: 1398
نوع سند: مقاله ژورنالی
زبان: English
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تاریخ نمایه سازی: 14 اردیبهشت 1400
Abstract:
A signed graph $(G,\sigma)$ is a graph together with an assignment of signs $\{+,-\}$ to its edges where $\sigma$ is the subset of its negative edges. There are a few variants of coloring and clique problems of signed graphs, which have been studied. An initial version known as vertex coloring of signed graphs is defined by Zaslavsky in $۱۹۸۲$. Recently Naserasr et. al., in [R. Naserasr, E. Rollova and E. Sopena, Homomorphisms of signed graphs, J. Graph Theory, ۷۹ (۲۰۱۵) ۱۷۸--۲۱۲, have defined signed chromatic and signed clique numbers of signed graphs. In this paper we consider the latter mentioned problems for signed interval graphs. We prove that the coloring problem of signed interval graphs is NP-complete whereas their ordinary coloring problem (the coloring problem of interval graphs) is in P. Moreover we prove that the signed clique problem of a signed interval graph can be solved in polynomial time. We also consider the complexity of further related problems.
Authors
Farzaneh Ramezani
Faculty of Mathematics, K. N. Toosi University of Technology, Tehran, Iran