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Displaying similar documents to “On Monochromatic Subgraphs of Edge-Colored Complete Graphs”

Coloring with no 2-colored P 4 's.

Albertson, Michael O., Chappell, Glenn G., Kierstead, H.A., Kündgen, André, Ramamurthi, Radhika (2004)

The Electronic Journal of Combinatorics [electronic only]

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A Note on Neighbor Expanded Sum Distinguishing Index

Evelyne Flandrin, Hao Li, Antoni Marczyk, Jean-François Saclé, Mariusz Woźniak (2017)

Discussiones Mathematicae Graph Theory

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A total k-coloring of a graph G is a coloring of vertices and edges of G using colors of the set [k] = {1, . . . , k}. These colors can be used to distinguish the vertices of G. There are many possibilities of such a distinction. In this paper, we consider the sum of colors on incident edges and adjacent vertices.

The set chromatic number of a graph

Gary Chartrand, Futaba Okamoto, Craig W. Rasmussen, Ping Zhang (2009)

Discussiones Mathematicae Graph Theory

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For a nontrivial connected graph G, let c: V(G)→ N be a vertex coloring of G where adjacent vertices may be colored the same. For a vertex v of G, the neighborhood color set NC(v) is the set of colors of the neighbors of v. The coloring c is called a set coloring if NC(u) ≠ NC(v) for every pair u,v of adjacent vertices of G. The minimum number of colors required of such a coloring is called the set chromatic number χₛ(G) of G. The set chromatic numbers of some well-known classes of graphs...

WORM Colorings of Planar Graphs

J. Czap, S. Jendrol’, J. Valiska (2017)

Discussiones Mathematicae Graph Theory

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Given three planar graphs F,H, and G, an (F,H)-WORM coloring of G is a vertex coloring such that no subgraph isomorphic to F is rainbow and no subgraph isomorphic to H is monochromatic. If G has at least one (F,H)-WORM coloring, then W−F,H(G) denotes the minimum number of colors in an (F,H)-WORM coloring of G. We show that (a) W−F,H(G) ≤ 2 if |V (F)| ≥ 3 and H contains a cycle, (b) W−F,H(G) ≤ 3 if |V (F)| ≥ 4 and H is a forest with Δ (H) ≥ 3, (c) W−F,H(G) ≤ 4 if |V (F)| ≥ 5 and H is...

Almost-Rainbow Edge-Colorings of Some Small Subgraphs

Elliot Krop, Irina Krop (2013)

Discussiones Mathematicae Graph Theory

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Let f(n, p, q) be the minimum number of colors necessary to color the edges of Kn so that every Kp is at least q-colored. We improve current bounds on these nearly “anti-Ramsey” numbers, first studied by Erdös and Gyárfás. We show that [...] , slightly improving the bound of Axenovich. We make small improvements on bounds of Erdös and Gyárfás by showing [...] and for all even n ≢ 1(mod 3), f(n, 4, 5) ≤ n− 1. For a complete bipartite graph G= Kn,n, we show an n-color construction to color...