Albertson's Conjecture on Crossing Numbers

Tessy Cardoz, Renukadevi.V, Malarvizhi.P

Abstract: In this paper, we prove the Albertson-s Conjecture which states that -If graph G has chromatic number r, then the crossing number of G is atleast that of the Kr- for 7 - r - 10 using results of Dirac, Gallai and Kostochka Stiebitz and Pach et al.

Keywords: Crossing number, complete graph, critical graph, lower bound