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pro vyhledávání: '"Brewster, Richard C"'
Given a graph $G=(V,E)$ of diameter $d$, a broadcast is a function $f:V(G) \to \{ 0, 1, \dots, d \}$ where $f(v)$ is at most the eccentricity of $v$. A vertex $v$ is broadcasting if $f(v)>0$ and a vertex $u$ hears $v$ if $d(u,v) \leq f(v)$. A broadca
Externí odkaz:
http://arxiv.org/abs/2406.05825
Autor:
Booker, Kyle, Brewster, Richard C
We present a edge-coloured analogue of the duality theorem for transitive tournaments and directed paths. Given a edge-coloured path $P$ whose edges alternate blue and red, we construct a edge-coloured graph $D$ so that for any edge-coloured graph $G
Externí odkaz:
http://arxiv.org/abs/2208.12326
Publikováno v:
Discrete Mathematics & Theoretical Computer Science, vol. 24, no 2, Graph Theory (November 3, 2022) dmtcs:9242
A mixed graph is a set of vertices together with an edge set and an arc set. An $(m,n)$-mixed graph $G$ is a mixed graph whose edges are each assigned one of $m$ colours, and whose arcs are each assigned one of $n$ colours. A \emph{switch} at a verte
Externí odkaz:
http://arxiv.org/abs/2203.08070
Autor:
Brewster, Richard C., Moore, Benjamin
Given a graph $G$, the $k$-mixing problem asks: Can one obtain all $k$-colourings of $G$, starting from one $k$-colouring $f$, by changing the colour of only one vertex at a time, while at each step maintaining a $k$-colouring? More generally, for a
Externí odkaz:
http://arxiv.org/abs/2008.12185
Autor:
Beaudou, Laurent, Brewster, Richard C.
Publikováno v:
Discrete Mathematics & Theoretical Computer Science, Vol. 21 no. 3 , Graph Theory (June 20, 2019) dmtcs:4452
In 2001, Erwin introduced broadcast domination in graphs. It is a variant of classical domination where selected vertices may have different domination powers. The minimum cost of a dominating broadcast in a graph $G$ is denoted $\gamma_b(G)$. The du
Externí odkaz:
http://arxiv.org/abs/1803.09639
Publikováno v:
Australasian Journal of Combinatorics 74(1):86-97, 2018
The dual concepts of coverings and packings are well studied in graph theory. Coverings of graphs with balls of radius one and packings of vertices with pairwise distances at least two are the well-known concepts of domination and independence, respe
Externí odkaz:
http://arxiv.org/abs/1803.02550
For a fixed graph $H$, the reconfiguration problem for $H$-colourings (i.e. homomorphisms to $H$) asks: given a graph $G$ and two $H$-colourings $\varphi$ and $\psi$ of $G$, does there exist a sequence $f_0,\dots,f_m$ of $H$-colourings such that $f_0
Externí odkaz:
http://arxiv.org/abs/1712.00200
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Publikováno v:
In Discrete Mathematics August 2021 344(8)
Publikováno v:
In Journal of Inorganic Biochemistry February 2021 215