Displaying similar documents to “Pattern hypergraphs.”

On planar mixed hypergraphs.

Dvořák, Zdeněk, Král, Daniel (2001)

The Electronic Journal of Combinatorics [electronic only]

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Chromatic Polynomials of Mixed Hypercycles

Julian A. Allagan, David Slutzky (2014)

Discussiones Mathematicae Graph Theory

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We color the vertices of each of the edges of a C-hypergraph (or cohypergraph) in such a way that at least two vertices receive the same color and in every proper coloring of a B-hypergraph (or bihypergraph), we forbid the cases when the vertices of any of its edges are colored with the same color (monochromatic) or when they are all colored with distinct colors (rainbow). In this paper, we determined explicit formulae for the chromatic polynomials of C-hypercycles and B-hypercycles ...

Three edge-coloring conjectures

Richard H. Schelp (2002)

Discussiones Mathematicae Graph Theory

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The focus of this article is on three of the author's open conjectures. The article itself surveys results relating to the conjectures and shows where the conjectures are known to hold.

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...

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.

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,...