On -bounded families of graphs.
Gyárfás, András, Zaker, Manouchehr (2011)
The Electronic Journal of Combinatorics [electronic only]
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Gyárfás, András, Zaker, Manouchehr (2011)
The Electronic Journal of Combinatorics [electronic only]
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Brualdi, Richard A., Mellendorf, Stephen (1994)
The Electronic Journal of Combinatorics [electronic only]
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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...
Caro, Yair, West, Douglas B. (2009)
The Electronic Journal of Combinatorics [electronic only]
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Eppstein, David (1999)
Journal of Graph Algorithms and Applications
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Xueliang Li, Ingo Schiermeyer, Kang Yang, Yan Zhao (2015)
Discussiones Mathematicae Graph Theory
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Let G be a nontrivial connected graph with an edge-coloring c : E(G) → {1, 2, . . . , q}, q ∈ ℕ, where adjacent edges may be colored the same. A tree T in G is called a rainbow tree if no two edges of T receive the same color. For a vertex set S ⊆ V (G), a tree that connects S in G is called an S-tree. The minimum number of colors that are needed in an edge-coloring of G such that there is a rainbow S-tree for every set S of k vertices of V (G) is called the k-rainbow index of G, denoted...
Carmi, Paz, Dujmovic, Vida, Morin, Pat, Wood, David R. (2008)
The Electronic Journal of Combinatorics [electronic only]
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Arge, Lars, Meyer, Ulrich, Toma, Laura, Zeh, Norbert (2003)
Journal of Graph Algorithms and Applications
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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...
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.
Dellamonica, Domingos jun., Kohayakawa, Yoshiharu (2008)
The Electronic Journal of Combinatorics [electronic only]
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Qiao, Sheng Ning (2010)
Applied Mathematics E-Notes [electronic only]
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