Ontology type: schema:ScholarlyArticle
2019-03-07
AUTHORSXin Zhang, Bei Niu, Jiguo Yu
ABSTRACTA graph is 1-planar if it can be drawn on a plane so that each edge is crossed by at most one other edge. In this paper, we first give a useful structural theorem for 1-planar graphs, and then apply it to the list edge and list total coloring, the (p, 1)-total labelling, and the equitable edge coloring of 1-planar graphs. More precisely, we verify the well-known List Edge Coloring Conjecture and List Total Coloring Conjecture for 1-planar graph with maximum degree at least 18, prove that the (p, 1)-total labelling number of every 1-planar graph G is at most Δ(G)+2p-2 provided that Δ(G)≥8p+2 and p≥2, and show that every 1-planar graph has an equitable edge coloring with k colors for any integer k≥18. These three results respectively generalize the main theorems of three different previously published papers. More... »
PAGES1-12
http://scigraph.springernature.com/pub.10.1007/s00373-019-02027-0
DOIhttp://dx.doi.org/10.1007/s00373-019-02027-0
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