A Characterization of Almost CIS Graphs

Wu, Yezhou; Zang, Wenan; Zhang, Cun-Quan

doi:10.1137/080723739

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Introduction3

A Characterization Of Split Graphs1

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Cited by 10 publications

(8 citation statements)

References 4 publications

(8 reference statements)

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“…The almost CIS graphs conicide with the split graphs with a unique split partition. This was conjectured by Boros et al [8] and proved by Wu et al [60].…”

Section: Introductionmentioning

confidence: 60%

See 1 more Smart Citation

On equistable, split, CIS, and related classes of graphs

Boros

Gurvich

Milanič

2017

Discrete Applied Mathematics

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“…The almost CIS graphs conicide with the split graphs with a unique split partition. This was conjectured by Boros et al [8] and proved by Wu et al [60].…”

Section: Introductionmentioning

confidence: 60%

“…The class of almost CIS graphs was introduced by Boros et al in [8] and characterized by Wu et al [60]. The characterization is based on split graphs.…”

Section: A Characterization Of Split Graphsmentioning

confidence: 99%

On equistable, split, CIS, and related classes of graphs

Boros

Gurvich

Milanič

2017

Discrete Applied Mathematics

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“…Localizable graphs form a subclass of wellcovered graphs [21,13], which are defined as graphs in which all maximal independent sets have the same size. A graph is said to be clique intersect stable set (CIS) if all of its maximal cliques are strong, or, equivalently, if all of its maximal independent sets are strong, see [4,3,22,5,12]. In other words, a graph is CIS if every maximal clique intersects every maximal independent set.…”

Section: Introductionmentioning

confidence: 99%

Strong cliques in vertex‐transitive graphs

Hujdurović

2020

Journal of Graph Theory

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“…The study of CIS graphs is rooted in observations of Berge [2] and Grillet [16] (see [33]). CIS graphs were studied in a series of papers [1,[3][4][5]11,12,[31][32][33]. The problem of recognizing CIS graphs is believed to be co-NP-complete [33], conjectured to be co-NP-complete [34], and conjectured to be polynomial [1].…”

Section: Introductionmentioning

confidence: 99%

Vertex-transitive CIS graphs

Dobson

Hujdurović

Milanič

et al. 2015

European Journal of Combinatorics

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A CIS graph is a graph in which every maximal stable set and every maximal clique intersect. A graph is well-covered if all its maximal stable sets are of the same size, co-well-covered if its complement is well-covered, and vertex-transitive if, for every pair of vertices, there exists an automorphism of the graph mapping one to the other. We show that a vertex-transitive graph is CIS if and only if it is well-covered, co-well-covered, and the product of its clique and stability numbers equals its order. A graph is irreducible if no two distinct vertices have the same neighborhood. We classify irreducible well-covered CIS graphs with clique number at most 3 and vertex-transitive CIS graphs of valency at most 7, which include an infinite family. We also exhibit an infinite family of vertex-transitive CIS graphs which are not Cayley

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A Characterization of Almost CIS Graphs

Cited by 10 publications

References 4 publications

On equistable, split, CIS, and related classes of graphs

On equistable, split, CIS, and related classes of graphs

Strong cliques in vertex‐transitive graphs

Vertex-transitive CIS graphs

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