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COMBINATORICS
2000
88views more  COMBINATORICS 2000»
13 years 9 months ago
Note on Sparse Random Graphs and Cover Graphs
It is shown in this note that with high probability it is enough to destroy all triangles in order to get a cover graph from a random graph Gn,p with p log n/n for any constant ...
Tom Bohman, Alan M. Frieze, Miklós Ruszink&...
COMBINATORICS
2000
49views more  COMBINATORICS 2000»
13 years 9 months ago
A Short Proof of a Partition Relation for Triples
We provide a much shorter proof of the following partition theorem of P. Erdos and R. Rado: If X is an uncountable linear order into which neither 1 nor 1 embeds, then X (, 4)3 f...
Albin L. Jones
COMBINATORICS
2000
71views more  COMBINATORICS 2000»
13 years 9 months ago
Diagonal Checker-jumping and Eulerian Numbers for Color-signed Permutations
Abstract. We introduce color-signed permutations to obtain a very explicit combinatorial interpretation of the q-Eulerian identities of Brenti and some generalizations. In particul...
Niklas Eriksen, Henrik Eriksson, Kimmo Eriksson
COMBINATORICS
2000
112views more  COMBINATORICS 2000»
13 years 9 months ago
A Note on Random Minimum Length Spanning Trees
Consider a connected r-regular n-vertex graph G with random independent edge lengths, each uniformly distributed on [0, 1]. Let mst(G) be the expected length of a minimum spanning...
Alan M. Frieze, Miklós Ruszinkó, Lub...
COMBINATORICS
2000
81views more  COMBINATORICS 2000»
13 years 9 months ago
Interchangeability of Relevant Cycles in Graphs
The set R of relevant cycles of a graph G is the union of its minimum cycle bases. We introduce a partition of R such that each cycle in a class W can be expressed as a sum of oth...
Petra M. Gleiss, Josef Leydold, Peter F. Stadler