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We show that any proper coloring of a Kneser graph $KG_{n,k}$ with $n-2k+2$ colors contains a trivial color (i.e., a color consisting of sets that all contain a fixed element), provided $n>(2+epsilon)k^2$, where $epsilonto 0$ as $kto infty$. This bound is essentially tight.
In this short note, we show that for any $epsilon >0$ and $k<n^{0.5-epsilon}$ the choice number of the Kneser graph $KG_{n,k}$ is $Theta (nlog n)$.
A proper edge-coloring of a graph $G$ with colors $1,ldots,t$ is called an emph{interval cyclic $t$-coloring} if all colors are used, and the edges incident to each vertex $vin V(G)$ are colored by $d_{G}(v)$ consecutive colors modulo $t$, where $d_{
An edge-coloring of a graph $G$ with consecutive integers $c_{1},ldots,c_{t}$ is called an emph{interval $t$-coloring} if all colors are used, and the colors of edges incident to any vertex of $G$ are distinct and form an interval of integers. A grap
$H_q(n,d)$ is defined as the graph with vertex set ${mathbb Z}_q^n$ and where two vertices are adjacent if their Hamming distance is at least $d$. The chromatic number of these graphs is presented for various sets of parameters $(q,n,d)$. For the $4$
For fixed positive integers $r, k$ and $ell$ with $1 leq ell < r$ and an $r$-uniform hypergraph $H$, let $kappa (H, k,ell)$ denote the number of $k$-colorings of the set of hyperedges of $H$ for which any two hyperedges in the same color class inters