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CPC
1998
154views more  CPC 1998»
13 years 7 months ago
Asymptotic Enumeration of Eulerian Circuits in the Complete Graph
We determine the asymptotic behaviour of the number of eulerian circuits in a complete graph of odd order. One corollary of our result is the following. If a maximum random walk, ...
Brendan D. McKay, Robert W. Robinson
DM
1998
73views more  DM 1998»
13 years 7 months ago
On constructing snakes in powers of complete graphs
We prove the conjecture of Abbott and Katchalski that for every m ≥ 2 there is a positive constant λm such that S(Kd mn) ≥ λmnd−1 S(Kd−1 m ) where S(Kd m) is the length o...
Jerzy Wojciechowski
EJC
2008
13 years 8 months ago
The distinguishing number of Cartesian products of complete graphs
The distinguishing number D(G) of a graph G is the least integer d such that G has a labeling with d labels that is preserved only by a trivial automorphism. We prove that Cartesi...
Wilfried Imrich, Janja Jerebic, Sandi Klavzar
ENDM
2007
74views more  ENDM 2007»
13 years 7 months ago
The order of the largest complete minor in a random graph
Let ccl(G) denote the order of the largest complete minor in a graph G (also called the contraction clique number) and let Gn,p denote a random graph on n vertices with edge probab...
Nikolaos Fountoulakis, Daniela Kühn, Deryk Os...
CCCG
2006
13 years 9 months ago
Geometric Separator for d-Dimensional Ball Graphs
We study the graph partitioning problem on ddimensional ball graphs in a geometric way. Let B be a set of balls in d-dimensional Euclidean space with radius ratio and -precision....
Kebin Wang, Shang-Hua Teng