### On graphs with isomorphic, non-isomorphic and connected ${N}_{2}$-neighbourhoods

Zdeněk Ryjáček (1987)

Časopis pro pěstování matematiky

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Zdeněk Ryjáček (1987)

Časopis pro pěstování matematiky

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Yousef Alavi, Don R. Lick, Song Lin Tian (1989)

Mathematica Slovaca

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Hazel Everett, Celina M. H. de Figueiredo, Sulamita Klein, Bruce Reed (2005)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

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The recently announced Strong Perfect Graph Theorem states that the class of perfect graphs coincides with the class of graphs containing no induced odd cycle of length at least 5 or the complement of such a cycle. A graph in this second class is called Berge. A bull is a graph with five vertices $x,a,b,c,d$ and five edges $xa,xb,ab,ad,bc$. A graph is bull-reducible if no vertex is in two bulls. In this paper we give a simple proof that every bull-reducible Berge graph is perfect. Although this result follows...

Zdeněk Ryjáček (1987)

Časopis pro pěstování matematiky

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S. Aparna Lakshmanan, S. B. Rao, A. Vijayakumar (2007)

Mathematica Bohemica

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The paper deals with graph operators—the Gallai graphs and the anti-Gallai graphs. We prove the existence of a finite family of forbidden subgraphs for the Gallai graphs and the anti-Gallai graphs to be $H$-free for any finite graph $H$. The case of complement reducible graphs—cographs is discussed in detail. Some relations between the chromatic number, the radius and the diameter of a graph and its Gallai and anti-Gallai graphs are also obtained.