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Graphs and Combinatorics

, Volume 23, Issue 6, pp 647–657 | Cite as

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

  • Michael A. Henning
  • Anders Yeo
Article

Abstract

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 \(\alpha'(G) \ge \min \left\{ \left( \frac{k^2 + 4}{k^2 + k + 2} \right) \times \frac{n}{2}, \frac{n-1}{2} \right\}\) , while if k is odd, then \(\alpha'(G) \ge \frac{(k^3-k^2-2) \, n - 2k + 2}{2(k^3-3k)}\) . We show that both bounds are tight.

Keywords

Lower bounds matching number regular graph 

AMS Subject Classification

05C70 

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Copyright information

© Springer-Verlag Tokyo 2007

Authors and Affiliations

  1. 1.School of Mathematical SciencesUniversity of KwaZulu-NatalPietermaritzburgSouth Africa
  2. 2.Department of Computer Science, Royal HollowayUniversity of LondonEgham SurreyUK

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