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2016

Local and global colorability of graphs

8 years 26 days ago
Local and global colorability of graphs
It is shown that for any fixed c ≥ 3 and r, the maximum possible chromatic number of a graph on n vertices in which every subgraph of radius at most r is c colorable is ˜Θ n 1 r+1 (that is, n 1 r+1 up to a factor poly-logarithmic in n). The proof is based on a careful analysis of the local and global colorability of random graphs and implies, in particular, that a random n-vertex graph with the right edge probability has typically a chromatic number as above and yet most balls of radius r in it are 2-degenerate.
Noga Alon, Omri Ben-Eliezer
Added 01 Apr 2016
Updated 01 Apr 2016
Type Journal
Year 2016
Where DM
Authors Noga Alon, Omri Ben-Eliezer
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