Hypergraphs with Pendant Paths are not Chromatically Unique

Ioan Tomescu

Displaying similar documents to “Hypergraphs with Pendant Paths are not Chromatically Unique”

Some results on chromatic polynomials of hypergraphs.

Walter, Manfred (2009)

The Electronic Journal of Combinatorics [electronic only]

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The Ramsey number of diamond-matchings and loose cycles in hypergraphs.

Gyárfás, András, Sárközy, Gábor N., Szemerédi, Endre (2008)

The Electronic Journal of Combinatorics [electronic only]

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On a theorem of Erdős, Rubin, and Taylor on choosability of complete bipartite graphs.

Kostochka, Alexandr (2002)

The Electronic Journal of Combinatorics [electronic only]

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Rainbow matching in edge-colored graphs.

LeSaulnier, Timothy D., Stocker, Christopher, Wenger, Paul S., West, Douglas B. (2010)

The Electronic Journal of Combinatorics [electronic only]

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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.

One More Turán Number and Ramsey Number for the Loose 3-Uniform Path of Length Three

Joanna Polcyn (2017)

Discussiones Mathematicae Graph Theory

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Let P denote a 3-uniform hypergraph consisting of 7 vertices a, b, c, d, e, f, g and 3 edges {a, b, c}, {c, d, e}, and {e, f, g}. It is known that the r-color Ramsey number for P is R(P; r) = r + 6 for r ≤ 9. The proof of this result relies on a careful analysis of the Turán numbers for P. In this paper, we refine this analysis further and compute the fifth order Turán number for P, for all n. Using this number for n = 16, we confirm the formula R(P; 10) = 16.

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 ...