On some conjectures of Graffiti

Béla Bollobás, Oliver Riordan
1998 Discrete Mathematics  
The computer program Galatea Gabriella Graffiti [8] made several conjectures concerning the chromatic numbers of graphs, related to the work of DeLaVina and Fajtlowicz [5] . We prove one of these conjectures, and disprove four. Returning to the property of k-colourability, in the original version of [5], DeLaVina and Fajtlowicz also listed several conjectures made by the conjecture making program Graffiti [8]. In this note we shall use random methods, and in particular a result of Bollob/ts and
more » ... Sauer [3] , to prove the existence of graphs with certain unexpected properties, which will disprove four of these conjectures.
doi:10.1016/s0012-365x(97)00093-9 fatcat:qbj7vlk2avajzdegvzmdf5jkte