Mar 13, 2013 · A \Sigma-coloring is a coloring of the elements of V so that vertices appearing together in some \Sigma(v) receive pairwise distinct colors. An ...

A Σ -coloring is a coloring of the elements of V so that vertices appearing together in some Σ ( v ) receive pairwise distinct colors. An obvious lower bound ...

Aug 31, 2011 · Theorem (Borodin, Ivanova, Neustroeva '08 & Ivanova '11). For any planar graph, χ2 =∆+1 in each of the following cases : g ≥ 24 and ∆ ≥ 3.

Sep 24, 2021 · A 2-distance k-coloring of a graph is a proper k-coloring of the vertices where vertices at distance at most 2 cannot share the same color.

A 2-distance k-coloring of a graph is a proper k-coloring of the vertices where vertices at distance at most 2 cannot share the same color.

Feb 27, 2014 · For graphs of bounded maximum average degree, we consider the problem of 2-distance coloring, that is, the problem of coloring the vertices ...

Feb 27, 2014 · A 2-distance k-coloring of a graph G is a coloring of the vertices of G with k colors such that two vertices that are adjacent or have a ...

A 2-distance list k-coloring of a graph is a proper coloring of the vertices where each vertex has a list of at least k available colors and vertices at ...

We prove that graphs with maximum average degree less than inline image and maximum degree Δ at least 4 are 2-distance inline image-colorable, which is optimal.

All the graphs we consider here are simple, finite and undirected. Let G = (V,E) be a graph. For any subgraph H of G, we denote V (H) and E(H) the.