Covering and partitioning of split, chain and cographs with isometric paths
D Chakraborty, H Müller, S Ordyniak… - … of Computer Science …, 2024 - drops.dagstuhl.de
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 𝒞 of a graph G is also an
isometric path partition if no vertex lies in two paths in 𝒞. 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.
collectively contain all vertices of G. An isometric path cover 𝒞 of a graph G is also an
isometric path partition if no vertex lies in two paths in 𝒞. 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.
[PDF][PDF] Covering and Partitioning of Split, Chain and Cographs with Isometric Paths
S Ordyniak, D Chakraborty, H Müller… - Leibniz …, 2024 - eprints.whiterose.ac.uk
Given a graph G, an isometric path cover of a graph is a set of isometric paths that
collectively 14 contain all vertices of G. An isometric path cover C of a graph G is also an
isometric path partition 15 if no vertex lies in two paths in C. Given a graph G, and an integer
k, the objective of Isometric 16 Path Cover (resp. Isometric Path Partition) is to decide
whether G has an isometric path 17 cover (resp. partition) of cardinality k. 18 In this paper,
we show that Isometric Path Partition is NP-complete even on split graphs, 19 ie graphs …
collectively 14 contain all vertices of G. An isometric path cover C of a graph G is also an
isometric path partition 15 if no vertex lies in two paths in C. Given a graph G, and an integer
k, the objective of Isometric 16 Path Cover (resp. Isometric Path Partition) is to decide
whether G has an isometric path 17 cover (resp. partition) of cardinality k. 18 In this paper,
we show that Isometric Path Partition is NP-complete even on split graphs, 19 ie graphs …
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