Almost all graphs have the conflict-free connection number 2. Even if we concentrate on regular graphs, from Theorem 1.2, Theorem 1.3 or 1.4, and the monotone property of c f c ( G ) , we also have the following result. For a fixed integer r ≥ 3 , almost all -regular graphs have the conflict-free connection number 2.
Sep 15, 2020
Oct 17, 2018 · An edge-colored graph G is conflict-free connected if every two of its vertices are connected by a path, which contains a color used on ...
Jul 6, 2017 · Abstract:An edge-colored graph G is \emph{conflict-free connected} if any two of its vertices are connected by a path, which contains a ...
May 8, 2018 · An edge-colored graph G is called conflict-free connected if each pair of distinct vertices is connected by a path which contains at least one ...
Oct 18, 2018 · An edge-colored graph $G$ is \emph{conflict-free connected} if any two of its vertices are connected by a path, which contains a color used ...
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May 21, 2021 · An edge-coloured graph G is called conflict-free connected if every two distinct vertices are connected by at least one path, which contains ...
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Graphs with Conflict-Free Connection Number Two. Lemma 4. If G is a 2-connected and non-complete graph, then cfc(G)=2. Proof. Since G contains non-adjacent ...
This vertex-colored graph is said to be conflict-free vertex-connected if every two distinct vertices of the graph are connected by a conflict-free path, and ...
An edge-coloured graph G is called conflict-free connected if every two distinct vertices are connected by at least one path, which contains a colour used ...
This paper investigates the conflict-free connection numbers of connected claw-free graphs, especially line graphs, using L(G) to denote the line graph of a ...