Výsledky vyhledávání - "Shook, James M."

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Packing a Degree Sequence Realization With A Graph

Autor: Shook, James M.

Two simple $n$-vertex graphs $G_{1}$ and $G_{2}$, with respective maximum degrees $\Delta_{1}$ and $\Delta_{2}$, are said to pack if $G_{1}$ is isomorphic to a subgraph of the complement of $G_{2}$. The BEC conjecture by Bollob\'{a}s, Eldridge, and C

Externí odkaz: http://arxiv.org/abs/2308.13130

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a characterization of the centers of chordal graphs

Autor: Shook, James M, Wei, Bing

A graph is $k$-chordal if it does not have an induced cycle with length greater than $k$. We call a graph chordal if it is $3$-chordal. Let $G$ be a graph. The distance between the vertices $x$ and $y$, denoted by $d_{G}(x,y)$, is the length of a sho

Externí odkaz: http://arxiv.org/abs/2210.00039

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On a conjecture that strengthens the $k$-factor case of Kundu's $k$-factor Theorem

Autor: Shook, James M.

In 1974, Kundu showed that for even $n$ if $\pi=(d_{1},\ldots,d_{n})$ is a non-increasing degree sequence such that $\mathcal{D}_{k}(\pi)=(d_{1}-k,\ldots,d_{n}-k)$ is graphic, then some realization of $\pi$ has a $k$-factor. In 1978, Brualdi and then

Externí odkaz: http://arxiv.org/abs/2205.01645

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Maximally Edge-Connected Realizations and Kundu's $k$-factor Theorem

Autor: Shook, James M.

A simple graph $G$ with edge-connectivity $\lambda(G)$ and minimum degree $\delta(G)$ is maximally edge connected if $\lambda(G)=\delta(G)$. In 1964, given a non-increasing degree sequence $\pi=(d_{1},\ldots,d_{n})$, Jack Edmonds showed that there is

Externí odkaz: http://arxiv.org/abs/2204.04299

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