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Motivated by the ErdH{o}s-Faber-Lovasz (EFL) conjecture for hypergraphs, we consider the list edge coloring of linear hypergraphs. We discuss several conjectures for list edge coloring linear hypergraphs that generalize both EFL and Vizings theorem for graphs. For example, we conjecture that in a linear hypergraph of rank 3, the list edge chromatic number is at most 2 times the maximum degree plus 1. We show that for sufficiently large fixed rank and sufficiently large degree, the conjectures are true.
Motivated by the Erdos-Faber Lovasz conjecture (EFL) for hypergraphs, we explore relationships between several conjectures on the edge coloring of linear hypergraphs. In particular, we are able to increase the class of hypergraphs for which EFL is true.
A strong edge-coloring of a graph $G$ is an edge-coloring such that any two edges on a path of length three receive distinct colors. We denote the strong chromatic index by $chi_{s}(G)$ which is the minimum number of colors that allow a strong edge-c
Let $G$ be a graph such that each edge has its list of available colors, and assume that each list is a subset of the common set consisting of $k$ colors. Suppose that we are given two list edge-colorings $f_0$ and $f_r$ of $G$, and asked whether the
An $r$-dynamic $k$-coloring of a graph $G$ is a proper $k$-coloring such that for any vertex $v$, there are at least $min{r, deg_G(v) }$ distinct colors in $N_G(v)$. The $r$-dynamic chromatic number $chi_r^d(G)$ of a graph $G$ is the least $k$ such t
Golovach, Paulusma and Song (Inf. Comput. 2014) asked to determine the parameterized complexity of the following problems parameterized by $k$: (1) Given a graph $G$, a clique modulator $D$ (a clique modulator is a set of vertices, whose removal resu