On Degree Sum Conditions and Vertex-Disjoint Chorded Cycles
نویسندگان
چکیده
منابع مشابه
On vertex-disjoint cycles and degree sum conditions
This paper considers a degree sum condition sufficient to imply the existence of k vertexdisjoint cycles in a graph G. For an integer t ≥ 1, let σt (G) be the smallest sum of degrees of t independent vertices of G. We prove that if G has order at least 7k+1 and σ4(G) ≥ 8k−3, with k ≥ 2, then G contains k vertex-disjoint cycles. We also show that the degree sum condition on σ4(G) is sharp and co...
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Very recently, Bialostocki et al. proposed the following conjecture. Let r, s be two nonnegative integers and let G = (V (G), E(G)) be a graph with |V (G)| ≥ 3r + 4s and minimum degree δ(G) ≥ 2r + 3s. Then G contains a collection of r cycles and s chorded cycles, all vertex-disjoint. We prove that this conjecture is true.
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ژورنال
عنوان ژورنال: Graphs and Combinatorics
سال: 2020
ISSN: 0911-0119,1435-5914
DOI: 10.1007/s00373-020-02227-z