Even Flow

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Finite groups have even more centralizers

For a finite group $G$‎, ‎let $Cent(G)$ denote the set of centralizers of single elements of $G$‎. ‎In this note we prove that if $|G|leq frac{3}{2}|Cent(G)|$ and $G$ is 2-nilpotent‎, ‎then $Gcong S_3‎, ‎D_{10}$ or $S_3times S_3$‎. ‎This result gives a partial and positive answer to a conjecture raised by A‎. ‎R‎. ‎Ashrafi [On finite groups with a given number of centralizers‎, ‎Algebra‎ ‎Collo...

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Making Even Swaps Even Easier

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Finding Even Cycles Even Faster

We describe efficient algorithms for finding even cycles in undirected graphs. Our main results are the following: (i) For every k ≥ 2, there is an O(V ) time algorithm that decides whether an undirected graph G = (V,E) contains a simple cycle of length 2k and finds one if it does. (ii) There is an O(V ) time algorithm that finds a shortest even cycle in an undirected graph G = (V,E).

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ژورنال

عنوان ژورنال: Arteriosclerosis, Thrombosis, and Vascular Biology

سال: 2005

ISSN: 1079-5642,1524-4636

DOI: 10.1161/01.atv.0000175755.93591.56