Zobrazeno 1 - 10
of 172
pro vyhledávání: '"Cameron, Ben"'
Autor:
Beaton, Iain, Cameron, Ben
A graph $G$ is $k$-vertex-critical if $\chi(G)=k$ but $\chi(G-v)
Externí odkaz:
http://arxiv.org/abs/2408.05027
A graph is $k$-vertex-critical if $\chi(G)=k$ but $\chi(G-v)
Externí odkaz:
http://arxiv.org/abs/2402.15908
We give an algorithm that finds a zero forcing set which approximates the optimal size by a factor of $\text{pw}(G)+1$, where $\text{pw}(G)$ is the pathwidth of $G$. Starting from a path decomposition, the algorithm runs in $O(nm)$ time, where $n$ an
Externí odkaz:
http://arxiv.org/abs/2402.08866
Autor:
Cameron, Ben, Hoàng, Chính T.
A graph is $k$-vertex-critical if $\chi(G)=k$ but $\chi(G-v)
Externí odkaz:
http://arxiv.org/abs/2306.03376
Autor:
Cameron, Ben, Hoàng, Chính T.
We give a new, stronger proof that there are only finitely many $k$-vertex-critical ($P_5$,~gem)-free graphs for all $k$. Our proof further refines the structure of these graphs and allows for the implementation of a simple exhaustive computer search
Externí odkaz:
http://arxiv.org/abs/2212.04659
Autor:
Beaton, Iain, Cameron, Ben
In this paper we study the the average order of dominating sets in a graph, $\operatorname{avd}(G)$. Like other average graph parameters, the extremal graphs are of interest. Beaton and Brown (2021) conjectured that for all graphs $G$ of order $n$ wi
Externí odkaz:
http://arxiv.org/abs/2208.10475
A graph $G$ is $k$-vertex-critical if $\chi(G)=k$ but $\chi(G-v)
Externí odkaz:
http://arxiv.org/abs/2206.03422
A cut-down de Bruijn sequence is a cyclic string of length $L$, where $1 \leq L \leq k^n$, such that every substring of length $n$ appears at most once. Etzion [Theor. Comp. Sci 44 (1986)] gives an algorithm to construct binary cut-down de Bruijn seq
Externí odkaz:
http://arxiv.org/abs/2205.02815
We consider the problem of listing all spanning trees of a graph $G$ such that successive trees differ by pivoting a single edge around a vertex. Such a listing is called a "pivot Gray code", and it has more stringent conditions than known "revolving
Externí odkaz:
http://arxiv.org/abs/2202.01746
We use a greedy strategy to list the spanning trees of the fan graph, $F_n$, such that successive trees differ by pivoting a single edge around a vertex. It is the first greedy algorithm for exhaustively generating spanning trees using such a minimal
Externí odkaz:
http://arxiv.org/abs/2108.09363