On a theorem of Kontsevich.
Conant, James, Vogtmann, Karen (2003)
Algebraic & Geometric Topology
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Conant, James, Vogtmann, Karen (2003)
Algebraic & Geometric Topology
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Gyárfás, András, Zaker, Manouchehr (2011)
The Electronic Journal of Combinatorics [electronic only]
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Diao, Guo-An, Feighn, Mark (2005)
Geometry & Topology
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Arge, Lars, Meyer, Ulrich, Toma, Laura, Zeh, Norbert (2003)
Journal of Graph Algorithms and Applications
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Brualdi, Richard A., Mellendorf, Stephen (1994)
The Electronic Journal of Combinatorics [electronic only]
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Eppstein, David (1999)
Journal of Graph Algorithms and Applications
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Bohdan Zelinka (1988)
Mathematica Slovaca
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Enkosky, Thomas (2011)
The Electronic Journal of Combinatorics [electronic only]
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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.
Ralph J. Faudree, Ronald J. Gould, Michael S. Jacobson (2013)
Discussiones Mathematicae Graph Theory
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For a fixed graph F, a graph G is F-saturated if there is no copy of F in G, but for any edge e ∉ G, there is a copy of F in G + e. The minimum number of edges in an F-saturated graph of order n will be denoted by sat(n, F). A graph G is weakly F-saturated if there is an ordering of the missing edges of G so that if they are added one at a time, each edge added creates a new copy of F. The minimum size of a weakly F-saturated graph G of order n will be denoted by wsat(n, F). The graphs...
Ziyu Hu, Ko-Wei Lih, Daphne Der-Fen Liu (2018)
Discussiones Mathematicae Graph Theory
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The strong chromatic index of a graph G, denoted by χ′s(G), is the minimum number of vertex induced matchings needed to partition the edge set of G. Let T be a tree without vertices of degree 2 and have at least one vertex of degree greater than 2. We construct a Halin graph G by drawing T on the plane and then drawing a cycle C connecting all its leaves in such a way that C forms the boundary of the unbounded face. We call T the characteristic tree of G. Let G denote a Halin graph with...