Optimal‐size clique transversals in chordal graphs | Zendy

Cooper Jacob W. | Zendy; Grzesik Andrzej | Zendy; Král' Daniel | Zendy

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Optimal‐size clique transversals in chordal graphs

Author(s) -

Cooper Jacob W.,

Grzesik Andrzej,

Král' Daniel

Publication year - 2018

Publication title -

journal of graph theory

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.164

H-Index - 54

eISSN - 1097-0118

pISSN - 0364-9024

DOI - 10.1002/jgt.22362

Subject(s) - combinatorics , mathematics , chordal graph , treewidth , clique sum , split graph , vertex (graph theory) , clique graph , discrete mathematics , clique , block graph , graph , pathwidth , 1 planar graph , line graph , graph power

The following question was raised by Tuza in 1990 and Erdős et al. in 1992: if every edge of an n ‐vertex chordal graph G is contained in a clique of size at least four, does G have a clique transversal, i.e. a set of vertices meeting all nontrivial maximal cliques, of size at most n / 4 ? We prove that every such graph G has a clique transversal of size at most 2 ( n − 1 ) / 7 if n ≥ 5 , which is the best possible bound.

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