TY - JOUR

T1 - On relating edges in graphs without cycles of length 4

AU - Levit, Vadim E.

AU - Tankus, David

PY - 2014/5

Y1 - 2014/5

N2 - An edge xy is relating in the graph G if there is an independent set S, containing neither x nor y, such that S? x and S? y are both maximal independent sets in G. It is an NP-complete problem to decide whether an edge is relating [1]. We show that the problem remains NP-complete even for graphs without cycles of lengths 4 and 5. On the other hand, we show that for graphs without cycles of lengths 4 and 6, the problem can be solved in polynomial time.

AB - An edge xy is relating in the graph G if there is an independent set S, containing neither x nor y, such that S? x and S? y are both maximal independent sets in G. It is an NP-complete problem to decide whether an edge is relating [1]. We show that the problem remains NP-complete even for graphs without cycles of lengths 4 and 5. On the other hand, we show that for graphs without cycles of lengths 4 and 6, the problem can be solved in polynomial time.

KW - Ford and Fulkerson algorithm

KW - Relating edge

KW - SAT problem

KW - Well-covered graph

UR - http://www.scopus.com/inward/record.url?scp=84899648842&partnerID=8YFLogxK

U2 - 10.1016/j.jda.2013.09.007

DO - 10.1016/j.jda.2013.09.007

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AN - SCOPUS:84899648842

SN - 1570-8667

VL - 26

SP - 28

EP - 33

JO - Journal of Discrete Algorithms

JF - Journal of Discrete Algorithms

ER -