Displaying similar documents to “An anti-Ramsey condition on trees.”

A decomposition of gallai multigraphs

Alexander Halperin, Colton Magnant, Kyle Pula (2014)

Discussiones Mathematicae Graph Theory

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An edge-colored cycle is rainbow if its edges are colored with distinct colors. A Gallai (multi)graph is a simple, complete, edge-colored (multi)graph lacking rainbow triangles. As has been previously shown for Gallai graphs, we show that Gallai multigraphs admit a simple iterative construction. We then use this structure to prove Ramsey-type results within Gallai colorings. Moreover, we show that Gallai multigraphs give rise to a surprising and highly structured decomposition into directed...

Total edge irregularity strength of trees

Jaroslav Ivančo, Stanislav Jendrol' (2006)

Discussiones Mathematicae Graph Theory

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A total edge-irregular k-labelling ξ:V(G)∪ E(G) → {1,2,...,k} of a graph G is a labelling of vertices and edges of G in such a way that for any different edges e and f their weights wt(e) and wt(f) are distinct. The weight wt(e) of an edge e = xy is the sum of the labels of vertices x and y and the label of the edge e. The minimum k for which a graph G has a total edge-irregular k-labelling is called the total edge irregularity strength of G, tes(G). In this paper we prove that...

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...

Vertex-distinguishing edge-colorings of linear forests

Sylwia Cichacz, Jakub Przybyło (2010)

Discussiones Mathematicae Graph Theory

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In the PhD thesis by Burris (Memphis (1993)), a conjecture was made concerning the number of colors c(G) required to edge-color a simple graph G so that no two distinct vertices are incident to the same multiset of colors. We find the exact value of c(G) - the irregular coloring number, and hence verify the conjecture when G is a vertex-disjoint union of paths. We also investigate the point-distinguishing chromatic index, χ₀(G), where sets, instead of multisets, are required to be distinct,...

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.

On rainbow trees and cycles.

Frieze, Alan, Krivelevich, Michael (2008)

The Electronic Journal of Combinatorics [electronic only]

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On the Vertex Folkman Numbers Fv(2,...,2;q)

Nenov, Nedyalko (2009)

Serdica Mathematical Journal

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2000 Mathematics Subject Classification: 05C55. In this paper we shall compute the Folkman numbers ... We prove also new bounds for some vertex and edge Folkman numbers.