Displaying similar documents to “On a theorem of Kontsevich.”

L(2, 1)-Labelings of Some Families of Oriented Planar Graphs

Sagnik Sen (2014)

Discussiones Mathematicae Graph Theory

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In this paper we determine, or give lower and upper bounds on, the 2-dipath and oriented L(2, 1)-span of the family of planar graphs, planar graphs with girth 5, 11, 16, partial k-trees, outerplanar graphs and cacti.

The structure of plane graphs with independent crossings and its applications to coloring problems

Xin Zhang, Guizhen Liu (2013)

Open Mathematics

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If a graph G has a drawing in the plane in such a way that every two crossings are independent, then we call G a plane graph with independent crossings or IC-planar graph for short. In this paper, the structure of IC-planar graphs with minimum degree at least two or three is studied. By applying their structural results, we prove that the edge chromatic number of G is Δ if Δ ≥ 8, the list edge (resp. list total) chromatic number of G is Δ (resp. Δ + 1) if Δ ≥ 14 and the linear arboricity...