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COMBINATORICS
2000

A Note on the Non-Colorability Threshold of a Random Graph

13 years 3 months ago
A Note on the Non-Colorability Threshold of a Random Graph
In this paper we consider the problem of establishing a value r0 such that almost all random graphs with n vertices and rn edges, r > r0, are asymptotically not 3-colorable. In our approach we combine the concept of rigid legal colorings introduced by Achlioptas and Molloy with the occupancy problem for random allocations of balls into bins. Using the sharp estimates obtained by Kamath et al. of the probability that no bin is empty after the random placement of the balls and exploiting the relationship between the placement of balls and the rigid legal colorings, we improve the value r0 = 2.522 previously obtained by Achlioptas and Molloy to r0 = 2.495.
Alexis C. Kaporis, Lefteris M. Kirousis, Yannis C.
Added 17 Dec 2010
Updated 17 Dec 2010
Type Journal
Year 2000
Where COMBINATORICS
Authors Alexis C. Kaporis, Lefteris M. Kirousis, Yannis C. Stamatiou
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