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Displaying similar documents to “Applying tabu search to determine new Ramsey graphs.”

On partitions of hereditary properties of graphs

Mieczysław Borowiecki, Anna Fiedorowicz (2006)

Discussiones Mathematicae Graph Theory

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In this paper a concept 𝓠-Ramsey Class of graphs is introduced, where 𝓠 is a class of bipartite graphs. It is a generalization of well-known concept of Ramsey Class of graphs. Some 𝓠-Ramsey Classes of graphs are presented (Theorem 1 and 2). We proved that 𝓣₂, the class of all outerplanar graphs, is not 𝓓₁-Ramsey Class (Theorem 3). This results leads us to the concept of acyclic reducible bounds for a hereditary property 𝓟 . For 𝓣₂ we found two bounds (Theorem 4). An improvement,...

Relating 2-Rainbow Domination To Roman Domination

José D. Alvarado, Simone Dantas, Dieter Rautenbach (2017)

Discussiones Mathematicae Graph Theory

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For a graph G, let R(G) and yr2(G) denote the Roman domination number of G and the 2-rainbow domination number of G, respectively. It is known that yr2(G) ≤ R(G) ≤ 3/2yr2(G). Fujita and Furuya [Difference between 2-rainbow domination and Roman domination in graphs, Discrete Appl. Math. 161 (2013) 806-812] present some kind of characterization of the graphs G for which R(G) − yr2(G) = k for some integer k. Unfortunately, their result does not lead to an algorithm that allows to recognize...

An attractive class of bipartite graphs

Rodica Boliac, Vadim Lozin (2001)

Discussiones Mathematicae Graph Theory

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In this paper we propose a structural characterization for a class of bipartite graphs defined by two forbidden induced subgraphs. We show that the obtained characterization leads to polynomial-time algorithms for several problems that are NP-hard in general bipartite graphs.

Some globally determined classes of graphs

Ivica Bošnjak, Rozália Madarász (2018)

Czechoslovak Mathematical Journal

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For a class of graphs we say that it is globally determined if any two nonisomorphic graphs from that class have nonisomorphic globals. We will prove that the class of so called CCB graphs and the class of finite forests are globally determined.

Dominant-matching graphs

Igor' E. Zverovich, Olga I. Zverovich (2004)

Discussiones Mathematicae Graph Theory

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We introduce a new hereditary class of graphs, the dominant-matching graphs, and we characterize it in terms of forbidden induced subgraphs.