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Jungho Ahn (안정호), Well-partitioned chordal graphs with the obstruction set and applications

April 27 Tuesday @ 4:30 PM - 5:30 PM KST

Room B232, IBS (기초과학연구원)


Jungho Ahn (안정호)
KAIST & IBS Discrete Mathematics Group

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.

This is joint work with Lars Jaffke, O-joung Kwon, and Paloma T. Lima.


April 27 Tuesday
4:30 PM - 5:30 PM KST
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Room B232
IBS (기초과학연구원)


Sang-il Oum (엄상일)
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IBS 이산수학그룹 Discrete Mathematics Group
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