Acyclic Chromatic Index of 1-Planar Graphs
Copyright policy )Acyclic Chromatic Index of 1-Planar Graphs
The acyclic chromatic index χa′(G) of a graph G is the smallest k for which G is a proper edge colorable using k colors. A 1-planar graph is a graph that can be drawn in plane such that every edge is crossed by at most one other edge. In this paper, we prove that every 1-planar graph G has χa′(G)≤Δ+36, where Δ denotes the maximum degree of G. This strengthens a result that if G is a triangle-free 1-planar graph, then χa′(G)≤Δ+16.
- Beijing University of Chinese Medicine China (People's Republic of)
- St. Francis Xavier University Canada
- Zhanjiang Normal University China (People's Republic of)
- Zhejiang Normal University China (People's Republic of)
- Weifang University China (People's Republic of)
discharging, QA1-939, 1-planar graph; acyclic edge coloring; acyclic chromatic index; discharging, acyclic edge coloring, acyclic chromatic index, 1-planar graph, Mathematics
discharging, QA1-939, 1-planar graph; acyclic edge coloring; acyclic chromatic index; discharging, acyclic edge coloring, acyclic chromatic index, 1-planar graph, Mathematics
citations This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).1 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Average influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Average impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Average
Citations provided by BIP!Popularity provided by BIP!