Alien Registration- Kierstead, Holly H. (Portland, Cumberland County)

https://digitalmaine.com/alien_docs/22155/thumbnail.jp

The (2k-1)-connected multigraphs with at most k-1 disjoint cycles

In 1963, Corr\'adi and Hajnal proved that for all $k \ge 1$ and $n \ge 3k$, every (simple) graph on n vertices with minimum degree at least 2k contains k disjoint cycles. The same year, Dirac described the 3-connected multigraphs not containing two disjoint cycles and asked the more general question: Which (2k-1)-connected multigraphs do not contain k disjoint cycles? Recently, the authors characterized the simple graphs G with minimum degree $\delta(G) \ge 2k-1$ that do not contain k disjoint cycles. We use this result to answer Dirac's question in full.Comment: 7 pages, 2 figures. To appear in Combinatoric