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An attractive class of bipartite graphs

Rodica Boliac, Vadim Lozin (2001)

Discussiones Mathematicae Graph Theory

In this paper we propose a structural characterization for a class of bipartite graphs defined by two forbidden induced subgraphs. We show that the obtained characterization leads to polynomial-time algorithms for several problems that are NP-hard in general bipartite graphs.

An elementary proof of a congruence by Skula and Granville

Romeo Meštrović (2012)

Archivum Mathematicum

Let p 5 be a prime, and let q p ( 2 ) : = ( 2 p - 1 - 1 ) / p be the Fermat quotient of p to base 2 . The following curious congruence was conjectured by L. Skula and proved by A. Granville q p ( 2 ) 2 - k = 1 p - 1 2 k k 2 ( mod p ) . In this note we establish the above congruence by entirely elementary number theory arguments.

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