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**public sources and our publisher partners.**Given a graph G, its triangular line graph is the graph T (G) with vertex set consisting of the edges of G and adjacencies between edges that are incident in G as well as being within a common… Expand

We study choosability with separation which is a constrained version of list coloring of graphs. A k,d-list assignment L of a graph G is a function that assigns to each vertex v a list Lv of at least… Expand

A distance graph is an undirected graph on the integers where two integers are adjacent if their difference is in a prescribed distance set. The independence ratio of a distance graph G is the… Expand

For a k -uniform hypergraph G with vertex set { 1 , ? , n } , the ordered Ramsey number OR t ( G ) is the least integer N such that every t -coloring of the edges of the complete k -uniform graph on… Expand

A star $k$-coloring is a proper $k$-coloring where the union of two color classes induces a star forest. While every planar graph is 4-colorable, not every planar graph is star 4-colorable. One… Expand

We present a refinement of Ramsey numbers by considering graphs with a partial ordering on their vertices. This is a natural extension of the ordered Ramsey numbers. We formalize situations in which… Expand

We introduce an ordered version of Ramsey numbers for hypergraphs using linearly ordered vertex sets. In this model, we obtain bounds on the ordered Ramsey numbers of the k-uniform hypergraph whose… Expand

The strong chromatic index of a graph $G$ , denoted $\chi'_s(G)$ , is the least number of colors needed to edge-color $G$ so that edges at distance at most two receive distinct colors. The strong… Expand