Changing of the domination number of a graph: edge multisubdivision and edge removal
Vladimir D. Samodivkin (2017)
Mathematica Bohemica
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Vladimir D. Samodivkin (2017)
Mathematica Bohemica
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Zaslavsky, Thomas (1998)
The Electronic Journal of Combinatorics [electronic only]
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Kolev, Nikolay (2008)
Serdica Mathematical Journal
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2000 Mathematics Subject Classification: 05C55. For a given graph G let V(G) and E(G) denote the vertex and the edge set of G respevtively. The symbol G e → (a1, …, ar) means that in every r-coloring of E(G) there exists a monochromatic ai-clique of color i for some i ∈ {1,…,r}. The edge Folkman numbers are defined by the equality Fe(a1, …, ar; q) = min{|V(G)| : G e → (a1, …, ar; q) and cl(G) < q}. In this paper we prove a new upper bound on the edge Folkman number...
Michael Andresen (2009)
Discussiones Mathematicae Graph Theory
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A comparability graph is a graph whose edges can be oriented transitively. Given a comparability graph G = (V,E) and an arbitrary edge ê∈ E we explore the question whether the graph G-ê, obtained by removing the undirected edge ê, is a comparability graph as well. We define a new substructure of implication classes and present a complete mathematical characterization of all those edges.
Brandes, Ulrik, Kääb, Vanessa, Löh, Andres, Wagner, Dorothea, Willhalm, Thomas (2000)
Journal of Graph Algorithms and Applications
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Július Czap, Peter Šugerek, Jaroslav Ivančo (2016)
Discussiones Mathematicae Graph Theory
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An edge coloring φ of a graph G is called an M2-edge coloring if |φ(v)| ≤ 2 for every vertex v of G, where φ(v) is the set of colors of edges incident with v. Let 𝒦2(G) denote the maximum number of colors used in an M2-edge coloring of G. In this paper we determine 𝒦2(G) for trees, cacti, complete multipartite graphs and graph joins.
Harary, Frank (2001)
Bulletin of the Malaysian Mathematical Sciences Society. Second Series
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U. J. Nieminen (1973)
Kybernetika
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Vladimir Boginski, Sergiy Butenko, Panos M. Pardalos (2004)
Computer Science and Information Systems
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J. Nieminen (1975)
Applicationes Mathematicae
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Izolda Gorgol (2005)
Discussiones Mathematicae Graph Theory
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The planar Ramsey number PR(G,H) is defined as the smallest integer n for which any 2-colouring of edges of Kₙ with red and blue, where red edges induce a planar graph, leads to either a red copy of G, or a blue H. In this note we study the weak induced version of the planar Ramsey number in the case when the second graph is complete.