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JOURNAL OF COMBINATORIAL THEORY 38. 93-94 (1985) Even Edge Colorings of a Graph
 

Summary: JOURNAL OF COMBINATORIAL THEORY 38. 93-94 (1985)
Note
Even Edge Colorings of a Graph
NOGA ALON
Department of Mathematics, Massachusetts Institute of Technology,
Cambridge, Massachusetts 02139
AND
YOSHIMI EGAWA
Department of Applied Mathematics, Science University of Tokvo,
Shinjuku-ku. Tokyo, 162 Japan
Communicated by the Managing Editors
Received April 30, 1984
It is shown that the minimum number of colors needed to paint the edges of a
graph G so that in every cycle of G there is a nonzero even number of edges of at
least one color is rlog,X(G)l. (" 1985 Academic Press, Inc.
For a simple graph G, let E(G) denote the minimum number 1for which
there exists a partition of E(G) into 1 subsets Ej, 1d id 1, satisfying
for any cycle Z of G, 0 < [E(Z) n Eil= 0 (mod 2)
for at least one Ei. (1)
The number obtained by replacing the condition (1) by

  

Source: Alon, Noga - School of Mathematical Sciences, Tel Aviv University

 

Collections: Mathematics