Sunflower hypergraphs are chromatically unique
نویسندگان
چکیده
منابع مشابه
Hypergraphs with pendant paths are not chromatically unique
In this note it is shown that every hypergraph containing a pendant path of length at least 2 is not chromatically unique. The same conclusion holds for h-uniform r-quasi linear 3-cycle if r ≥ 2.
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An h-uniform hypergraph (h ≥ 2) H = (V, E) of order n = |V| and size m = |E|, consists of a vertex set V(H) = V and edge set E(H) = E , where E ⊂ V and |E| = h for each edge E in E . H is said to be linear if 0 ≤ |E ∩ F | ≤ 1 for any two distinct edges E,F ∈ E(H) [1]. Let P h,1 p denote the linear path consisting of p ≥ 1 edges E1, . . . , Ep such that |E1| = . . . = |Ep| = h, |Ek ∩ El| = 1 if ...
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Let θ(a1, a2, · · · , ak) denote the graph obtained by connecting two distinct vertices with k independent paths of lengths a1, a2, · · · , ak respectively. Assume that 2 ≤ a1 ≤ a2 ≤ · · · ≤ ak. We prove that the graph θ(a1, a2, · · · , ak) is chromatically unique if ak < a1 + a2, and find examples showing that θ(a1, a2, · · · , ak) may not be chromatically unique if ak = a1 + a2.
متن کاملClasses of chromatically unique graphs
Borowiecki, M. and E. Drgas-Burchardt, Classes of chromatically unique graphs, Discrete Mathematics Ill (1993) 71-75. We prove that graphs obtained from complete equibipartite graphs by deleting some independent sets of edges are chromatically unique. 1. Preliminary definitions and results In this paper we consider finite, undirected, simple and loopless graphs. Two graphs G and H are said to b...
متن کاملChromatic polynomials of some sunflower mixed hypergraphs
The theory of mixed hypergraph coloring was first introduced by Voloshin in 1993 and has been growing ever since. The proper coloring of a mixed hypergraph H = (X, C,D) is the coloring of the vertex set X so that no D-hyperedge is monochromatic and no C-hyperedge is polychromatic. A mixed hypergraph with hyperedges of type D, C or B is commonly known as a D, C, or B-hypergraph respectively wher...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2004
ISSN: 0012-365X
DOI: 10.1016/j.disc.2004.02.015