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A Survey of Best Monotone Degree Conditions for Graph Properties

Autor: Bauer, D., Broersma, H. J., Heuvel, J. van den, Kahl, N., Nevo, A., Schmeichel, E., Woodall, D. R., Yatauro, M.

We survey sufficient degree conditions, for a variety of graph properties, that are best possible in the same sense that Chvatal's well-known degree condition for hamiltonicity is best possible.
Comment: 25 pages

Externí odkaz: http://arxiv.org/abs/1405.5760

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Degree Sequences and the Existence of $k$-Factors

Autor: Bauer, D., Broersma, H. J., Heuvel, J. van den, Kahl, N., Schmeichel, E.

We consider sufficient conditions for a degree sequence $\pi$ to be forcibly $k$-factor graphical. We note that previous work on degrees and factors has focused primarily on finding conditions for a degree sequence to be potentially $k$-factor graphi

Externí odkaz: http://arxiv.org/abs/0912.2916

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Toughness and Vertex Degrees

Autor: Bauer, D., Broersma, H. J., Heuvel, J. van den, Kahl, N., Schmeichel, E.

We study theorems giving sufficient conditions on the vertex degrees of a graph $G$ to guarantee $G$ is $t$-tough. We first give a best monotone theorem when $t\ge1$, but then show that for any integer $k\ge1$, a best monotone theorem for $t=\frac1k\

Externí odkaz: http://arxiv.org/abs/0912.2919

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