Tight Lower Bounds on the Size of a Maximum Matching in a Regular Graph

Authors:
Michael A. Henning;Anders Yeo
Affiliations:
University of KwaZulu-Natal, School of Mathematical Sciences, 3209, Pietermaritzburg, South Africa;University of London, Department of Computer Science, Royal Holloway, TW20 OEX, Egham Surrey, UK
Venue:
Graphs and Combinatorics
Year:
2007

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Abstract

In this paper we study tight lower bounds on the size of amaximum matching in a regular graph. For k ≥ 3, letG be a connected k-regular graph of order nand let a'(G) be the size of a maximum matching inG. We show that if k is even, then α'(G) ≥min {(k2+4 / k2+k+2)} xn/2 , n-1/2}, while if k is odd, thenα(G) ≤(k3-k2-2)n-2k+2 /2(k3-3k). We show that both bounds are tight.