Displaying similar documents to “Paths through fixed vertices in edge-colored graphs”

Adjacent vertex distinguishing edge colorings of the direct product of a regular graph by a path or a cycle

Laura Frigerio, Federico Lastaria, Norma Zagaglia Salvi (2011)

Discussiones Mathematicae Graph Theory

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In this paper we investigate the minimum number of colors required for a proper edge coloring of a finite, undirected, regular graph G in which no two adjacent vertices are incident to edges colored with the same set of colors. In particular, we study this parameter in relation to the direct product of G by a path or a cycle.

Rainbow Connection Number of Graphs with Diameter 3

Hengzhe Li, Xueliang Li, Yuefang Sun (2017)

Discussiones Mathematicae Graph Theory

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A path in an edge-colored graph G is rainbow if no two edges of the path are colored the same. The rainbow connection number rc(G) of G is the smallest integer k for which there exists a k-edge-coloring of G such that every pair of distinct vertices of G is connected by a rainbow path. Let f(d) denote the minimum number such that rc(G) ≤ f(d) for each bridgeless graph G with diameter d. In this paper, we shall show that 7 ≤ f(3) ≤ 9.

Fruit salad.

Gyárfás, András (1997)

The Electronic Journal of Combinatorics [electronic only]

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A proof of the two-path conjecture.

Fleischner, Herbert, Molina, Robert R., Smith, Ken W., West, Douglas B. (2002)

The Electronic Journal of Combinatorics [electronic only]

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