Results 31 to 40 of about 4,035 (167)
Matchings with few colors in colored complete graphs and hypergraphs
Discrete Mathematics, 2020 Abstract The t -color Ramsey problem for hypergraph matchings was settled by the well-known result of Alon, Frankl and Lovasz (answering a conjecture of Erdős). This result was the last step in a chain of special cases most notably Lovasz’s solution to Kneser’s problem. We proposed an extension of the Erdős problem: for given 1 ≤ s ≤ t
Gábor N. Sárközy +2 more
openaire +2 more sources
Toric algebra of hypergraphs [PDF]
, 2013 The edges of any hypergraph parametrize a monomial algebra called the edge subring of the hypergraph. We study presentation ideals of these edge subrings, and describe their generators in terms of balanced walks on hypergraphs.
Petrović, Sonja, Stasi, Despina
core +1 more source
The 1-2-3 Conjecture for Hypergraphs [PDF]
, 2016 A weighting of the edges of a hypergraph is called vertex-coloring if the weighted degrees of the vertices yield a proper coloring of the graph, i.e., every edge contains at least two vertices with different weighted degrees.
Kalkowski, Maciej +2 more
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Colored complete hypergraphs containing no rainbow Berge triangles
Theory and Applications of Graphs, 2019 The study of graph Ramsey numbers within restricted colorings, in particular forbidding a rainbow triangle, has recently been blossoming under the name GallaiRamsey numbers.
Colton Magnant
semanticscholar +1 more source
Rainbow Coloring Hardness via Low Sensitivity Polymorphisms [PDF]
, 2019 A k-uniform hypergraph is said to be r-rainbow colorable if there is an r-coloring of its vertices such that every hyperedge intersects all r color classes.
Guruswami, Venkatesan, Sandeep, Sai
core +1 more source
Chromatic Ramsey number of acyclic hypergraphs [PDF]
, 2015 Suppose that $T$ is an acyclic $r$-uniform hypergraph, with $r\ge 2$. We define the ($t$-color) chromatic Ramsey number $\chi(T,t)$ as the smallest $m$ with the following property: if the edges of any $m$-chromatic $r$-uniform hypergraph are colored with
Gyárfás, András +2 more
core +2 more sources
Color-blind index in graphs of very low degree [PDF]
, 2015 Let $c:E(G)\to [k]$ be an edge-coloring of a graph $G$, not necessarily proper. For each vertex $v$, let $\bar{c}(v)=(a_1,\ldots,a_k)$, where $a_i$ is the number of edges incident to $v$ with color $i$.
Achlioptas +13 more
core +3 more sources
On Hypergraph and Graph Isomorphism with Bounded Color Classes [PDF]
, 2006 Using logspace counting classes we study the computational complexity of hypergraph and graph isomorphism where the vertex sets have bounded color classes for certain specific bounds. We also give a polynomial-time algorithm for hypergraph isomorphism for bounded color classes of arbitrary size.
Vikraman Arvind, Johannes Köbler
openaire +2 more sources
Distributed Symmetry Breaking in Hypergraphs
, 2014 Fundamental local symmetry breaking problems such as Maximal Independent Set (MIS) and coloring have been recognized as important by the community, and studied extensively in (standard) graphs.
A. Ephremides +16 more
core +1 more source
Super-polylogarithmic hypergraph coloring hardness via low-degree long codes
, 2013 We prove improved inapproximability results for hypergraph coloring using the low-degree polynomial code (aka, the 'short code' of Barak et. al. [FOCS 2012]) and the techniques proposed by Dinur and Guruswami [FOCS 2013] to incorporate this code for ...
Guruswami, Venkatesan +4 more
core +1 more source