منابع مشابه
Uniquely colorable mixed hypergraphs
A mixed hypergraph consists of two families of edges: the C-edges and D-edges. In a coloring every C-edge has at least two vertices of the same color, while every D-edge has at least two vertices colored differently. The largest and smallest possible numbers of colors in a coloring are termed the upper and lower chromatic number, χ̄ and χ, respectively. A mixed hypergraph is called uniquely colo...
متن کاملOrderings of uniquely colorable hypergraphs
For a mixed hypergraphH= (X,C,D), where C andD are set systems over the vertex set X, a coloring is a partition of X into ‘color classes’such that everyC ∈ Cmeets some class in more than one vertex, and everyD ∈ D has a nonempty intersection with at least two classes.A vertex-order x1, x2, . . . , xn onX (n=|X|) is uniquely colorable if the subhypergraph induced by {xj : 1 j i} has precisely on...
متن کاملdecomposing hypergraphs into k-colorable hypergraphs
for a given hypergraph $h$ with chromatic number $chi(h)$ and with no edge containing only one vertex, it is shown that the minimum number $l$ for which there exists a partition (also a covering) ${e_1,e_2,ldots,e_l}$ for $e(h)$, such that the hypergraph induced by $e_i$ for each $1leq ileq l$ is $k$-colorable, is $lceil log_{k} chi(h) rceil$.
متن کاملHardness of Finding Independent Sets in 2-Colorable and Almost 2-Colorable Hypergraphs
This work studies the hardness of finding independent sets in hypergraphs which are either 2colorable or are almost 2-colorable, i.e. can be 2-colored after removing a small fraction of vertices and the incident hyperedges. To be precise, say that a hypergraph is (1−ε)-almost 2-colorable if removing an ε fraction of its vertices and all hyperedges incident on them makes the remaining hypergraph...
متن کاملExtremal Problems for t-Partite and t-Colorable Hypergraphs
Fix integers t ≥ r ≥ 2 and an r-uniform hypergraph F . We prove that the maximum number of edges in a t-partite r-uniform hypergraph on n vertices that contains no copy of F is ct,F ( n r ) + o(nr), where ct,F can be determined by a finite computation. We explicitly define a sequence F1, F2, . . . of r-uniform hypergraphs, and prove that the maximum number of edges in a t-chromatic r-uniform hy...
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ژورنال
عنوان ژورنال: Theoretical Computer Science
سال: 2019
ISSN: 0304-3975
DOI: 10.1016/j.tcs.2019.09.010