32 research outputs found
The strong chromatic index of 1-planar graphs
The chromatic index of a graph is the smallest for which
admits an edge -coloring such that any two adjacent edges have distinct
colors. The strong chromatic index of is the smallest such
that has a proper edge -coloring with the condition that any two edges
at distance at most 2 receive distinct colors. A graph is 1-planar if it can be
drawn in the plane so that each edge is crossed by at most one other edge.
In this paper, we show that every graph with maximum average degree
has . As a corollary, we
prove that every 1-planar graph with maximum degree has
, which improves a result, due to Bensmail et
al., which says that if