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» On the Grundy Number of a Graph
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JGT
2010
113views more  JGT 2010»
13 years 6 months ago
Crossing numbers of imbalanced graphs
The crossing number, cr(G), of a graph G is the least number of crossing points in any drawing of G in the plane. According to the Crossing Lemma of Ajtai, Chv´atal, Newborn, Sze...
János Pach, József Solymosi, G&aacut...
COMBINATORICS
2006
126views more  COMBINATORICS 2006»
13 years 7 months ago
Bounding the Number of Edges in Permutation Graphs
Given an integer s 0 and a permutation Sn, let ,s be the graph on n vertices {1, . . . , n} where two vertices i < j are adjacent if the permutation flips their order and th...
Peter Keevash, Po-Shen Loh, Benny Sudakov
ARSCOM
2008
103views more  ARSCOM 2008»
13 years 7 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»
14 years 2 months 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»
13 years 9 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....