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SODA
2003
ACM
103views Algorithms» more  SODA 2003»
15 years 7 months ago
On the rectilinear crossing number of complete graphs
We prove a lower bound of 0.3288   n 4¡ for the rectilinear crossing number cr(Kn) of a complete graph on n vertices, or in other words, for the minimum number of convex quadril...
Uli Wagner
TCS
2008
15 years 6 months ago
Setting port numbers for fast graph exploration
We consider the problem of periodic graph exploration by a finite automaton in which an automaton with a constant number of states has to explore all unknown anonymous graphs of a...
David Ilcinkas
JGT
2010
113views more  JGT 2010»
15 years 4 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»
15 years 6 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»
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