Geodesic
All regular multigraphs of even order and high degree are 1-factorable
The electronic journal of combinatorics, Tome 8 (2001) no. 1
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Plantholt and Tipnis (1991) proved that for any even integer $r$, a regular multigraph $G$ with even order $n$, multiplicity $\mu(G) \leq r$ and degree high relative to $n$ and $r$ is 1-factorable. Here we extend this result to include the case when $r$ is any odd integer. Häggkvist and Perković and Reed (1997) proved that the One-factorization Conjecture for simple graphs is asymptotically true. Our techniques yield an extension of this asymptotic result on simple graphs to a corresponding asymptotic result on multigraphs.
DOI : 10.37236/1585
Classification : 05C70, 05C40
Mots-clés : regular multigraph, one-factorization conjecture 
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     title = {All regular multigraphs of even order and high degree are 1-factorable},
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     year = {2001},
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     number = {1},
     doi = {10.37236/1585},
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Michael J. Plantholt; Shailesh K. Tipnis. All regular multigraphs of even order and high degree are 1-factorable. The electronic journal of combinatorics, Tome 8 (2001) no. 1. doi: 10.37236/1585

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