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Martin Milanič, Tree Decompositions with Bounded Independence Number

Friday, November 5, 2021 @ 4:30 PM - 5:30 PM KST

Zoom ID: 869 4632 6610 (ibsdimag)

Speaker

The independence number of a tree decomposition $\mathcal{T}$ of a graph is the smallest integer $k$ such that each bag of $\mathcal{T}$ induces a subgraph with independence number at most $k$. If a graph $G$ is given together with a tree decomposition with bounded independence number, then the Maximum Weight Independent Set (MWIS) problem can be solved in polynomial time. Motivated by this observation, we consider six graph containment relations—the subgraph, topological minor, and minor relations, as well as their induced variants—and for each of them characterize the graphs $H$ for which any graph excluding $H$ with respect to the relation admits a tree decomposition with bounded independence number. Furthermore, using a variety of tools including SPQR trees and potential maximal cliques, we show how to obtain such tree decompositions efficiently.

As an immediate consequence, we obtain that the MWIS problem can be solved in polynomial time in an infinite family of graph classes that properly contain the class of chordal graphs. In fact, our approach shows that the Maximum Weight Independent $\mathcal{H}$-Packing problem, a common generalization of the MWIS and the Maximum Weight Induced Matching problems, can be solved in polynomial time in these graph classes.

This is joint work with Clément Dallard and Kenny Štorgel.

Details

Date:
Friday, November 5, 2021
Time:
4:30 PM - 5:30 PM KST
Event Category:
Event Tags:

Venue

Zoom ID: 869 4632 6610 (ibsdimag)

Organizer

O-joung Kwon (권오정)
IBS 이산수학그룹 Discrete Mathematics Group
기초과학연구원 수리및계산과학연구단 이산수학그룹
대전 유성구 엑스포로 55 (우) 34126
IBS Discrete Mathematics Group (DIMAG)
Institute for Basic Science (IBS)
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