Graphs with forbidden subgraphs
نویسندگان
چکیده
منابع مشابه
Graphs with Forbidden Subgraphs
Many graphs which are encountered in the study of graph theory are characterized by a type of configuration or subgraph they possess. However, there are occasions when such graphs are more easily defined or described by the kind of subgraphs they are not permitted to contain. For example, a tree can be defined as a connected graph which contains no cycles, and Kuratowski [22] characterized plan...
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The graph theoretic problem of identifying the finite sets C of constraint graphs for which there is a countable universal C-free graph is closely related to the problem of determining for which sets C the model companion T ∗ C of the theory of C-free graphs is א0-categorical, and this leads back to combinatorics. Little is known about these theories from any other perspective, such as stabilit...
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For every real p > 0 and simple graph G, set f (p,G) = ∑ u∈V (G) d (u) , and let φ (r, p, n) be the maximum of f (p,G) taken over all Kr+1-free graphs G of order n. We prove that, if 0 < p < r, then φ (r, p, n) = f (p, Tr (n)) , where Tr (n) is the r-partite Turan graph of order n. For every p ≥ r + ⌈√ 2r ⌉ and n large, we show that φ (p, n, r) > (1 + ε) f (p, Tr (n)) for some ε = ε (r) > 0. Ou...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series B
سال: 1971
ISSN: 0095-8956
DOI: 10.1016/0095-8956(71)90065-7