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Intersection number of two connected geometric graphs

✍ Scribed by Shin-ichi Tokunaga


Book ID
107766324
Publisher
Elsevier Science
Year
1996
Tongue
English
Weight
285 KB
Volume
59
Category
Article
ISSN
0020-0190

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πŸ“œ SIMILAR VOLUMES


Intersection number and capacities of gr
✍ J. KΓΆrner πŸ“‚ Article πŸ“… 1995 πŸ› Elsevier Science 🌐 English βš– 955 KB

For an arbitrary graph G we determine the asymptotics of the intersection number (edgeclique covering number) of the categorical (or weak) product of G and the complete graph K,, asymptotically in n. The result follows from a more general theorem on graph capacities which generalizes an earlier resu

On the stability number of the edge inte
✍ Claudio Arbib; Alberto Caprara πŸ“‚ Article πŸ“… 2002 πŸ› Elsevier Science 🌐 English βš– 38 KB

Let G be the graph obtained as the edge intersection of two graphs G 1 , G 2 on the same vertex set V . We show that if at , where Ξ±() is the cardinality of the largest stable set. Moreover, for general G 1 and G 2 , we show that Ξ±(G) R(Ξ±(G 1 ) + 1, Ξ±(G 2 ) + 1) -1, where R(k, ) is the Ramsey numbe

Powers of geometric intersection graphs
✍ Geir Agnarsson; Peter Damaschke; MagnΓΊs M. HalldΓ³rsson πŸ“‚ Article πŸ“… 2003 πŸ› Elsevier Science 🌐 English βš– 188 KB

We study powers of certain geometric intersection graphs: interval graphs, m-trapezoid graphs and circular-arc graphs. We deΓΏne the pseudo-product, (G; G ) β†’ G \* G , of two graphs G and G on the same set of vertices, and show that G \* G is contained in one of the three classes of graphs mentioned

The number of connected sparsely edged g
✍ E. M. Wright πŸ“‚ Article πŸ“… 1977 πŸ› John Wiley and Sons 🌐 English βš– 472 KB

## Abstract An (__n, q__) graph has __n__ labeled points, __q__ edges, and no loops or multiple edges. The number of connected (__n, q__) graphs is __f(n, q)__. Cayley proved that __f(n, n__^‐1^) = __n__^nβˆ’2^ and Renyi found a formula for __f(n, n)__. Here I develop two methods to calculate the exp