Degree powers in graphs with a forbidden forest
نویسندگان
چکیده
منابع مشابه
Degree Powers in Graphs with Forbidden Subgraphs
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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Let Cl denote the cycle of length l: For p 2 and integer k 1; we prove that the function (k; p; n) = max <: X u2V (G) d (u) : G is a graph of order n containing no C2k+2 =; satis es (k; p; n) = knp (1 + o (1)) : This settles a conjecture of Caro and Yuster. Our proof is based on a new su¢ cient condition for long paths, that may be useful in other applications as well.
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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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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2019
ISSN: 0012-365X
DOI: 10.1016/j.disc.2018.11.013