Perfectly orderable graphs and unique colorability | Zendy

Gábor Bacsó | Zendy

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Perfectly orderable graphs and unique colorability

Author(s) -

Gábor Bacsó

Publication year - 2007

Publication title -

applicable analysis and discrete mathematics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.69

H-Index - 26

eISSN - 2406-100X

pISSN - 1452-8630

DOI - 10.2298/aadm0702415b

Subject(s) - combinatorics , mathematics , clique graph , split graph , perfect graph , vertex (graph theory) , block graph , graph , discrete mathematics , clique , independent set , chordal graph , graph power , line graph , 1 planar graph

Given a linear order < on the vertices of a graph, an obstruction is an induced P4 abcd such that a < b and d < c. A linear order without any obstruction is called perfect. A graph is perfectly orderable if its vertex set has some perfect order. In the graph G, for two vertices x and y, x clique-dominates y if every maximum size clique containing y, contains x too. We prove the following result: If a perfectly orderable graph is clique-pair-free then it contains two vertices such that one of them clique-dominates the other one.

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