## May 13, 2016:

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A note on acyclic edge coloring of complete bipartite graphs

## By Manu Basavaraju and L. Sunil Chandran

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Presented by Siddharth Gupta

Abstract : An acyclic edge coloring of a graph is a proper edge coloring
such that there are no bichromatic (2-colored) cycles. The acyclic chromatic
index of a graph is the minimum number k such that there is an acyclic edge
coloring using k colors and is denoted by a'(G).
In this paper, the authors prove that a'(Kp,p) = p+2 = Delta+2 when p is
prime. They also show that if we remove any edge from Kp,p, the
resulting graph is acyclically Delta + 1 = p + 1-edge-colorable.