On the quantum chromatic number of a graph.
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On the recognition of bipolarizable and -simplicial graphs.
Nikolopoulos, Stavros D., Palios, Leonidas (2005)
Discrete Mathematics and Theoretical Computer Science. DMTCS [electronic only]
On the Steiner 2-edge connected subgraph polytope
A. Rhida Mahjoub, Pierre Pesneau (2008)
RAIRO - Operations Research
In this paper, we study the Steiner 2-edge connected subgraph polytope. We introduce a large class of valid inequalities for this polytope called the generalized Steiner F-partition inequalities, that generalizes the so-called Steiner F-partition inequalities. We show that these inequalities together with the trivial and the Steiner cut inequalities completely describe the polytope on a class of graphs that generalizes the wheels. We also describe necessary conditions for these inequalities to...
On the Vertex Separation of Cactus Graphs
Markov, Minko (2007)
Serdica Journal of Computing
This paper is part of a work in progress whose goal is to construct a fast, practical algorithm for the vertex separation (VS) of cactus graphs. We prove a theorem for cacti", a necessary and sufficient condition for the VS of a cactus graph being k. Further, we investigate the ensuing ramifications that prevent the construction of an algorithm based on that theorem only.
On the Zagreb index of quasi-tree graphs.
Qiao, Sheng Ning (2010)
Applied Mathematics E-Notes [electronic only]
One-factorizations of regular graphs of order 12.
Kaski, Petteri, Östergård, Patric R.J. (2005)
The Electronic Journal of Combinatorics [electronic only]
On-line 𝓟-coloring of graphs
Piotr Borowiecki (2006)
Discussiones Mathematicae Graph Theory
For a given induced hereditary property 𝓟, a 𝓟-coloring of a graph G is an assignment of one color to each vertex such that the subgraphs induced by each of the color classes have property 𝓟. We consider the effectiveness of on-line 𝓟-coloring algorithms and give the generalizations and extensions of selected results known for on-line proper coloring algorithms. We prove a linear lower bound for the performance guarantee function of any stingy on-line 𝓟-coloring algorithm. In the class of generalized...
Operations on directed graphs.
Jürgen Eufinger (1971)
Journal für die reine und angewandte Mathematik
Optimal double-loop networks with non-unit steps.
Aguiló, F., Simó, E., Zaragozá, M. (2003)
The Electronic Journal of Combinatorics [electronic only]
Optimal edge ranking of complete bipartite graphs in polynomial time
Ruo-Wei Hung (2006)
Discussiones Mathematicae Graph Theory
An edge ranking of a graph is a labeling of edges using positive integers such that all paths connecting two edges with the same label visit an intermediate edge with a higher label. An edge ranking of a graph is optimal if the number of labels used is minimum among all edge rankings. As the problem of finding optimal edge rankings for general graphs is NP-hard [12], it is interesting to concentrate on special classes of graphs and find optimal edge rankings for them efficiently. Apart from trees...
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