TY - JOUR

T1 - The Structure of Well-Covered Graphs and the Complexity of Their Recognition Problems

AU - Tankus, David

AU - Tarsi, Michael

N1 - Funding Information:
* Research supported in part by the Fund for Basic Research administered by the Israel Academy of Sciences. E-mail: tarsi math.tau.ac.il.

PY - 1997/3

Y1 - 1997/3

N2 - A graph is well-covered if all its maximal independent sets are of the same cardinality. Deciding whether a given graph is well-covered is known to beNP-hard in general, and solvable in polynomial time, if the input is restricted to certain families of graphs. We present here a simple structural characterization of well-covered graphs and then apply it to the recognition problem. Apparently, polynomial algorithms become easier to design. In particular we present a new polynomial time algorithm for the case where the input graph contains no induced subgraph isomorphic toK1, 3. Considering the line-graph of an input graph, this result provides a short and simple alternative to a proof by Lesk, Plummer and Pulleyblank, who showed that equimatchable graphs can be recognized in polynomial time.

AB - A graph is well-covered if all its maximal independent sets are of the same cardinality. Deciding whether a given graph is well-covered is known to beNP-hard in general, and solvable in polynomial time, if the input is restricted to certain families of graphs. We present here a simple structural characterization of well-covered graphs and then apply it to the recognition problem. Apparently, polynomial algorithms become easier to design. In particular we present a new polynomial time algorithm for the case where the input graph contains no induced subgraph isomorphic toK1, 3. Considering the line-graph of an input graph, this result provides a short and simple alternative to a proof by Lesk, Plummer and Pulleyblank, who showed that equimatchable graphs can be recognized in polynomial time.

UR - http://www.scopus.com/inward/record.url?scp=0008994723&partnerID=8YFLogxK

U2 - 10.1006/jctb.1996.1742

DO - 10.1006/jctb.1996.1742

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AN - SCOPUS:0008994723

SN - 0095-8956

VL - 69

SP - 230

EP - 233

JO - Journal of Combinatorial Theory. Series B

JF - Journal of Combinatorial Theory. Series B

IS - 2

ER -