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DTSTART;TZID=Asia/Seoul:20210427T163000
DTEND;TZID=Asia/Seoul:20210427T173000
DTSTAMP:20260419T024743
CREATED:20210419T130854Z
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SUMMARY:Jungho Ahn (안정호)\, Well-partitioned chordal graphs with the obstruction set and applications
DESCRIPTION:We introduce a new subclass of chordal graphs that generalizes split graphs\, which we call well-partitioned chordal graphs. Split graphs are graphs that admit a partition of the vertex set into cliques that can be arranged in a star structure\, the leaves of which are of size one. Well-partitioned chordal graphs are a generalization of this concept in the following two ways. First\, the cliques in the partition can be arranged in a tree structure\, and second\, each clique is of arbitrary size. We mainly provide a characterization of well-partitioned chordal graphs by forbidden induced subgraphs and give a polynomial-time algorithm that given any graph\, either finds an obstruction or outputs a partition of its vertex set that asserts that the graph is well-partitioned chordal. We demonstrate the algorithmic use of this graph class by showing that two variants of the problem of finding pairwise disjoint paths between k given pairs of vertices are in FPT\, parameterized by k\, on well-partitioned chordal graphs\, while on chordal graphs\, these problems are only known to be in XP. From the other end\, we introduce some problems that are polynomial-time solvable on split graphs but become NP-complete on well-partitioned chordal graphs. \nThis is joint work with Lars Jaffke\, O-joung Kwon\, and Paloma T. Lima.
URL:https://dimag.ibs.re.kr/event/2021-04-27/
LOCATION:Room B232\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
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