Results 1 to 10 of about 4,011 (115)
Cartesian product of hypergraphs: properties and algorithms [PDF]
Electronic Proceedings in Theoretical Computer Science, 2009 Cartesian products of graphs have been studied extensively since the 1960s. They make it possible to decrease the algorithmic complexity of problems by using the factorization of the product.
Alain Bretto +2 more
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Bounded colorings of multipartite graphs and hypergraphs
European Journal of Combinatorics, 2017 Let $c$ be an edge-coloring of the complete $n$-vertex graph $K_n$. The problem of finding properly colored and rainbow Hamilton cycles in $c$ was initiated in 1976 by Bollob s and Erd\H os and has been extensively studied since then. Recently it was extended to the hypergraph setting by Dudek, Frieze and Ruci ski. We generalize these results, giving
Kamčev, Nina +2 more
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Scheduling Problems and Generalized Graph Coloring [PDF]
Discrete Mathematics & Theoretical Computer Science, 2020 We define a new type of vertex coloring which generalizes vertex coloring in graphs, hypergraphs, andsimplicial complexes. To this coloring there is an associated symmetric function in noncommuting variables for whichwe give a deletion-contraction ...
John Machacek
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Zero-Free Intervals of Chromatic Polynomials of Mixed Hypergraphs
Mathematics, 2022 A mixed hypergraph H is a triple (X,C,D), where X is a finite set and each of C and D is a family of subsets of X. For any positive integer λ, a proper λ-coloring of H is an assignment of λ colors to vertices in H such that each member in C contains at ...
Ruixue Zhang +2 more
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Adapted List Coloring of Graphs and Hypergraphs [PDF]
SIAM Journal on Discrete Mathematics, 2008 We introduce and study adapted list coloring of graphs and hypergraphs. This is a generalization of ordinary list coloring and adapted coloring, and has more applications than these. We prove that the upper bounds on the adaptable choosability of graphs and uniform hypergraphs in terms of maximum degree are sufficiently stronger than those on the ...
A. V. Kostochka, Xuding Zhu
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A Theoretical Investigation Based on the Rough Approximations of Hypergraphs
Journal of Mathematics, 2022 Rough sets are a key tool to model uncertainty and vagueness using upper and lower approximations without predefined functions and additional suppositions.
Musavarah Sarwar
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On splittable colorings of graphs and hypergraphs [PDF]
Journal of Graph Theory, 2002 AbstractThe notion of a split coloring of a complete graph was introduced by Erdős and Gyárfás [7] as a generalization of split graphs. In this work, we offer an alternate interpretation by comparing such a coloring to the classical Ramsey coloring problem via a two‐round game played against an adversary.
Füredi, Zoltán, Ramamurthi, Radhika
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Local k-colorings of graphs and hypergraphs
Journal of Combinatorial Theory, Series B, 1987 A local k-coloring of a graph is a coloring of its edges such that the edges incident with any vertex are colored with at most k different colors. In this paper similarities and differences between usual and local k-coloring are investigated with respect to Ramsey type problems.
Gyárfás, A +5 more
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On the connectivity of proper colorings of random graphs and hypergraphs
Random Structures & Algorithms, 2020 Let Ωq=Ωq(H) denote the set of proper [q]‐colorings of the hypergraph H. Let Γq be the graph with vertex set Ωq where two colorings σ,τ are adjacent iff the corresponding colorings differ in exactly one vertex. We show that if H=Hn,m;k, k ≥ 2, the random k‐uniform hypergraph with V=[n] and m=dn/k hyperedges then w.h.p.
Anastos, Michael, Frieze, Alan
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Graphs with coloring redundant edges
Electronic Journal of Graph Theory and Applications, 2016 A graph edge is $d$-coloring redundant if the removal of the edge doesnot change the set of $d$-colorings of the graph. Graphs that are toosparse or too dense do not have coloring redundant edges.
Bart Demoen, Phuong-Lan Nguyen
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