# Alain Hertz & University of Mons Graph Day talk

Hadrien Melot organized a very pleasant one day conference at the University of Mons on Tuesday. I talked about “A Difficult Graph for Independence Number Theory” (here are the slides).

With Alain Hertz in the audience I hoped to find a forbidden subgraph characterization for the efficient calculation of the independence number that I didn’t previously know – or maybe a new technique that could be used to efficiently reduce the order of the graph for which independence number is calculated. He didn’t let me down. He suggested that the graph in question may be “skew star”-free (a skew star is $S_{1,2,3}$). I think he is correct – but we’ll write code, to check, and add this test to INP. Hertz and collaborators proved that there is an efficient algorithm for independence number in skew-star free graphs. His paper is here.