Gallai-Milgram properties for infinite graphs
نویسندگان
چکیده
منابع مشابه
Gallai graphs and anti-Gallai graphs
The Gallai graph and the anti-Gallai graph of a graph G have the edges of G as their vertices. Two edges of G are adjacent in the Gallai graph of G if they are incident but do not span a triangle in G; they are adjacent in the anti-Gallai graph of G if they span a triangle in G. In this paper we show: The Four Color Theorem can be equivalently stated in terms of anti-Gallai graphs; the problems...
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This chapter deals with two graph classes the Gallai graphs and the anti-Gallai graphs. \Ve construct infinitely many pairs of graphs G and H such that f( G) = r( H). The existence of a finite family offorbidden subgraphs for the Gallai graphs and the ant.i-Gallai graphs to be H-frce, for any fillit.e graph H is proved and the forbidden subgraph characterizations of G for which the Gallai graph...
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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 it...
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Let G(∞) be an infinite graph with the vertex set corresponding to the set of positive integers N. Denote by G(l) a subgraph of G(∞) which is spanned by the vertices {1, . . . , l}. As a possible extension of Turán’s theorem to infinite graphs, in this paper we will examine how large lim inf l→∞ |E(G(l))| l2 can be for an infinite graph G(∞), which does not contain an increasing path Ik with k ...
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We investigate graphs with the property that all longest paths or all longest cycles have empty intersection. In this paper, we find such graphs as subgraphs of cubic lattices.
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1991
ISSN: 0012-365X
DOI: 10.1016/0012-365x(91)90328-y