Journal Issue10.1002/JGT.V43:1
2-connected 7-coverings of 3-connected graphs on surfaces
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TL;DR: In this article, it was shown that every 3-connected graph on a surface with Euler genus k ≥ 2 with sufficiently large representativity has a 2-connected 7-covering with at most 6k-12 vertices of degree 7.
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Abstract: An m-covering of a graph G is a spanning subgraph of G with maximum degree at most m. In this paper, we shall show that every 3-connected graph on a surface with Euler genus k ≥ 2 with sufficiently large representativity has a 2-connected 7-covering with at most 6k - 12 vertices of degree 7. We also construct, for every surface F2 with Euler genus k ≥ 2, a 3-connected graph G on F2 with arbitrarily large representativity each of whose 2-connected 7-coverings contains at least 6k - 12 vertices of degree 7. © 2003 Wiley Periodicals, Inc. J Graph Theory 43: 26–36, 2003
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- 01 Jan 2006
TL;DR: Extensions and variations of the notion of edge-connectivity of undirected graphs, directed graphs, and hypergraphs will be considered and classical results concerning orientations and connectivity augmentations may be formulated in this more general setting.
How Many Conjectures Can You Stand? A Survey
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References
•Book
Graph theory with applications
J. A. Bondy
- 01 Jan 1976
TL;DR: In this paper, the authors present Graph Theory with Applications: Graph theory with applications, a collection of applications of graph theory in the field of Operational Research and Management. Journal of the Operational research Society: Vol. 28, Volume 28, issue 1, pp. 237-238.
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On eulerian and hamiltonian graphs and line graphs
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362
A Reduction Method for Edge-Connectivity in Graphs
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345
On a Closure Concept in Claw-Free Graphs
TL;DR: A sufficient condition for claw-free graphs, the equivalence of some conjectures on hamiltonicity in 2-tough graphs, and the corresponding conjectures for 7-connected claw free graphs are obtained as corollaries in this paper.
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