Hang-Yip Liu, Steffen Schulze, et al.
Proceedings of SPIE - The International Society for Optical Engineering
Let G = (V, E) be any d-regular graph with girth g on n vertices, for d ≥ 3. This note shows that G has a maximum matching which includes all but an exponentially small fraction of the vertices, O((d - 1)-g/2). Specifically, in a maximum matching of G, the number of unmatched vertices is at most n/n0(d, g), where n0(d, g) is the number of vertices in a ball of radius [(g - 1)/2] around a vertex, for odd values of g, and around an edge, for even values of g. This result is tight if n < 2n 0(d, g).
Hang-Yip Liu, Steffen Schulze, et al.
Proceedings of SPIE - The International Society for Optical Engineering
Daniel J. Costello Jr., Pierre R. Chevillat, et al.
ISIT 1997
George Markowsky
J. Math. Anal. Appl.
L Auslander, E Feig, et al.
Advances in Applied Mathematics