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» Grundy number and products of graphs
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DAM
2008
67views more  DAM 2008»
13 years 7 months ago
On the variance of Shannon products of graphs
We study the combinatorial problem of finding an arrangement of distinct integers into the ddimensional N-cube so that the maximal variance of the numbers on each -dimensional sec...
József Balogh, Clifford D. Smyth
COMBINATORICS
2000
85views more  COMBINATORICS 2000»
13 years 7 months ago
Inequality Related to Vizing's Conjecture
Let (G) denote the domination number of a graph G and let G H denote the Cartesian product of graphs G and H. We prove that (G)(H) 2(G H) for all simple graphs G and H. 2000 Math...
W. Edwin Clark, Stephen Suen
ITA
2007
104views Communications» more  ITA 2007»
13 years 7 months ago
Automata, Borel functions and real numbers in Pisot base
This note is about functions f : Aω → Bω whose graph is recognized by a B¨uchi finite automaton on the product alphabet A × B. These functions are Baire class 2 in the Bair...
Benoit Cagnard, Pierre Simonnet
DM
2007
97views more  DM 2007»
13 years 7 months ago
Recognizing Cartesian products in linear time
We present an algorithm that determines the prime factors of connected graphs with respect to the Cartesian product in linear time and space. This improves a result of Aurenhammee...
Wilfried Imrich, Iztok Peterin
CPC
2007
76views more  CPC 2007»
13 years 7 months ago
Strong Isometric Dimension, Biclique Coverings, and Sperner's Theorem
The strong isometric dimension of a graph G is the least number k such that G isometrically embeds into the strong product of k paths. Using Sperner’s Theorem, the strong isomet...
Dalibor Froncek, Janja Jerebic, Sandi Klavzar, Pet...