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pro vyhledávání: '"Goddard, Wayne"'
For a graph with colored vertices, a rainbow subgraph is one where all vertices have different colors. For graph $G$, let $c_k(G)$ denote the maximum number of different colors in a coloring without a rainbow path on $k$ vertices, and $cp_k(G)$ the m
Externí odkaz:
http://arxiv.org/abs/2501.01302
Autor:
Boyer, Geoffrey, Goddard, Wayne
An isolating set in a graph is a set $X$ of vertices such that every edge of the graph is incident with a vertex of $X$ or its neighborhood. The isolation number of a graph, or equivalently the vertex-edge domination number, is the minimum number of
Externí odkaz:
http://arxiv.org/abs/2401.03933
Autor:
Goddard, Wayne
We show that there are 2-tough 4-regular graphs with claws
Externí odkaz:
http://arxiv.org/abs/2301.13632
Publikováno v:
In Applied Mathematics and Computation 1 September 2024 476
We define a $P$-compelling coloring as a proper coloring of the vertices of a graph such that every subset consisting of one vertex of each color has property $P$. The $P$-compelling chromatic number is the minimum number of colors in such a coloring
Externí odkaz:
http://arxiv.org/abs/2105.03694
Autor:
Goddard, Wayne, VanLandingham, Julia
Publikováno v:
In Discrete Applied Mathematics 30 January 2024 343:82-90
Motivated by the concept of well-covered graphs, we define a graph to be well-bicovered if every vertex-maximal bipartite subgraph has the same order (which we call the bipartite number). We first give examples of them, compare them with well-covered
Externí odkaz:
http://arxiv.org/abs/1909.07503