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ARSCOM
2008
103views more  ARSCOM 2008»
15 years 6 months ago
Estimating the number of graphs containing very long induced paths
Let P(n, k) denote the number of graphs on n + k vertices that contain Pn, a path on n vertices, as an induced subgraph. In this note we will find upper and lower bounds for P(n, ...
Steven Butler
LION
2009
Springer
125views Optimization» more  LION 2009»
16 years 16 days ago
New Bounds on the Clique Number of Graphs Based on Spectral Hypergraph Theory
This work introduces new bounds on the clique number of graphs derived from a result due to S´os and Straus, which generalizes the Motzkin-Straus Theorem to a specific class of h...
Samuel Rota Bulò, Marcello Pelillo
ESA
2008
Springer
127views Algorithms» more  ESA 2008»
15 years 7 months ago
The Alcuin Number of a Graph
We consider a planning problem that generalizes Alcuin's river crossing problem (also known as: The wolf, goat, and cabbage puzzle) to scenarios with arbitrary conflict graph...
Péter Csorba, Cor A. J. Hurkens, Gerhard J....
EJC
2008
15 years 6 months ago
Fractional chromatic number of distance graphs generated by two-interval sets
Let D be a set of positive integers. The distance graph generated by D, denoted by G(Z, D), has the set Z of all integers as the vertex Supported in part by the National Science ...
Daphne Der-Fen Liu, Xuding Zhu
JGT
2007
85views more  JGT 2007»
15 years 5 months ago
On graphs with subgraphs having large independence numbers
: Let G be a graph on n vertices in which every induced subgraph on s = log3 n vertices has an independent set of size at least t = log n. What is the largest q = q(n) so that ever...
Noga Alon, Benny Sudakov