Tight lower bounds on the matching number in a graph with given maximum degree
نویسندگان
چکیده
منابع مشابه
Tight Lower Bounds on the Size of a Maximum Matching in a Regular Graph
In this paper we study tight lower bounds on the size of a maximum matching in a regular graph. For k ≥ 3, let G be a connected k-regular graph of order n and let α′(G) be the size of a maximum matching in G. We show that if k is even, then α′(G) ≥ min {( k2+4 k2+k+2 ) × n2 , n−1 2 } , while if k is odd, then α′(G) ≥ (k3−k2−2) n−2k+2 2(k3−3k) . We show that both bounds are tight.
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ژورنال
عنوان ژورنال: Journal of Graph Theory
سال: 2018
ISSN: 0364-9024
DOI: 10.1002/jgt.22244