Covering and Partitioning of Split, Chain and Cographs with Isometric Paths
Given a graph G, an isometric path cover of a graph is a set of isometric paths that collectively contain all vertices of G. An isometric path cover đť’ž of a graph G is also an isometric path partition if no vertex lies in two paths in đť’ž. Given a graph G, and an integer k, the objective of Isometric Path Cover (resp. Isometric Path Partition) is to decide whether G has an isometric path cover (resp. partition) of cardinality k.
In this paper, we show that Isometric Path Partition is NP-complete even on split graphs, i.e. graphs whose vertex set can be partitioned into a clique and an independent set. In contrast, we show that both Isometric Path Cover and Isometric Path Partition admit polynomial time algorithms on cographs (graphs with no induced Pâ‚„) and chain graphs (bipartite graphs with no induced 2Kâ‚‚).
Isometric path partition (cover)
chordal graphs
chain graphs
split graphs
Theory of computation~Graph algorithms analysis
39:1-39:14
Regular Paper
Dibyayan
Chakraborty
Dibyayan Chakraborty
School of Computing, University of Leeds, UK
https://orcid.org/0000-0003-0534-6417
Haiko
MĂĽller
Haiko MĂĽller
School of Computing, University of Leeds, UK
https://orcid.org/0000-0002-1123-1774
Sebastian
Ordyniak
Sebastian Ordyniak
School of Computing, University of Leeds, UK
https://orcid.org/0000-0003-1935-651X
Fahad
Panolan
Fahad Panolan
School of Computing, University of Leeds, UK
https://orcid.org/0000-0001-6213-8687
Mateusz
Rychlicki
Mateusz Rychlicki
School of Computing, University of Leeds, UK
https://orcid.org/0000-0002-8318-2588
10.4230/LIPIcs.MFCS.2024.39
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Dibyayan Chakraborty, Haiko MĂĽller, Sebastian Ordyniak, Fahad Panolan, and Mateusz Rychlicki
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