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ARSCOM
2008
118views more  ARSCOM 2008»
13 years 11 months ago
Proper Partitions of a Polygon and k-Catalan Numbers
Let P be a polygon whose vertices have been colored (labeled) cyclically with the numbers 1, 2, . . . , c. Motivated by conjectures of Propp, we are led to consider partitions of ...
Bruce E. Sagan
ARSCOM
2008
98views more  ARSCOM 2008»
13 years 11 months ago
New Sufficient Conditions for s-Hamiltonian Graphs and s-Hamiltonian Connected Graphs
Yan Jin, Kewen Zhao, Hong-Jian Lai, Ju Zhou
ARSCOM
2008
103views more  ARSCOM 2008»
13 years 11 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
ARSCOM
2008
192views more  ARSCOM 2008»
13 years 11 months ago
Bounds on the metric and partition dimensions of a graph
Given a graph G, we say S V (G) is resolving if for each pair of distinct u, v V (G) there is a vertex x in S where d(u, x) = d(v, x). The metric dimension of G is the minimum c...
Glenn G. Chappell, John G. Gimbel, Chris Hartman
ARSCOM
2008
119views more  ARSCOM 2008»
13 years 11 months ago
Greedy Defining Sets in Latin Squares
A Greedy Defining Set is a set of entries in a Latin square with the property that when the square is systematically filled in with a greedy algorithm, the greedy algorithm succee...
Manouchehr Zaker