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 -