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Some Advances on Greedy Colorings

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					Some Advances on Greedy Colorings

  a
Cl´udia Linhares Sales
UFC

Resumo/Abstract:
Given a graph G = (V, E), a k-coloring c of G is assignment of
colors {1, . . . , k} to the vertices of G in such way that c(v) = c(u)
for any edge uv ∈ E(G). We say that c is a greedy k-coloring if for
each vertex v ∈ V , colors 1, 2 . . . , i − 1 occur in the neighborhood
of v wherever c(v) = i. The Grundy number of G, Γ(G), is the
biggest k such that G admits a greedy k-coloring. Determining
Γ(G) is N P -hard for general graphs. In this talk, besides some
classical results, we will present some facts on the behavior of Γ(G)
when G is the lexicographic product between two graphs G1 and
G2 , in terms of Γ(G1 ) and Γ(G2 ). In particular, we will show that
Γ(G1 ) × Γ(G2 ) ≤ Γ(G1 [G2 ]) ≤ 2Γ(G1 )−1 (Γ(G2 ) − 1) + Γ(G1 ) − 1
                             e
(join work with M. Ast´ and F. Havet). Moreover, we present a
polynomial algorithm to determine Γ(G) when G is a extended P4 -
laden or a fat extended P4 -laden, giving a general strategy for using
the modular decomposition of a graph to determining its Grundy
number (join work with J. Ara´jo).  u

				
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posted:2/24/2010
language:English
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