סמינר מחלקתי

Dominating induced matchings in graphs containing no long claw

Alain Hertz
Polytechnique Montréal, Canada

(Coauthors : V. Lozin, B. Ries, V. Zamaraev, D. de Werra)

Abstract:

An induced matching M in a graph G is dominating if every edge not in M shares exactly one vertex with an edge in M. The dominating induced matching problem (also known as efficient edge domination) asks whether a graph G contains a dominating induced matching. This problem is generally NP-complete, but polynomial-time solvable for graphs with some special properties. In particular, it is solvable in polynomial time for claw-free graphs.

We study this problem for graphs containing no long claw, i.e. no induced subgraph obtained from the claw by subdividing each of its edges exactly once. To solve the problem in this class, we reduce it to the following question: given a graph G and a subset of its vertices, does G contain a matching saturating all vertices of the subset? We show that this question can be answered in polynomial time, thus providing a polynomial-time algorithm to solve the dominating induced matching problem for graphs containing no long claw.

Bio :

Holder of a diploma in Mathematical Engineering, Alain Hertz obtained a Ph.D in operations research at the École Polytechnqiue Fédérale de Lausanne. Since 2001, he is professor at the department of mathematics and industrial engineering at the École Polytechnique in Montréal. He is also member of the multi disciplinary GERAD research group that includes nearly sixty researchers and experts in operations research and discrete mathematics.

He is the author of about 180 scientific publications His main research domains are combinatorial optimization, graph theory, algorithmics, and the development of decision aid systems for scheduling and distribution problems.

ההרצאה תתקיים ביום שלישי 20.10.15, בשעה 14:00 בחדר 206, בנין וולפסון הנדסה, הפקולטה להנדסה, אוניברסיטת תל-אביב.