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Title: Regular multigraphs of high degree and even order are 1-factorable
Prof. Shailesh Tipnis, Illinois State University
Date & Time: June 28, 2010 10:00
Venue: Seminar Hall, Old CSE Building
Abstract:
A regular multigraph with maximum edge multiplicity r and degree rs cannot always be factored into r s-regular simple graphs. We show that under general conditions such a factorization can be obtained if we allow the deletion or addition of a relatively small number of hamilton cycles. Based on this result and a result about 1-factorability of simple graphs of high degree we prove that regular multigraphs of high degree and even order are 1-factorable. We point out that this verifies the Seymour-Goldberg multigraph edge-coloring conjecture for such multigraphs.
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