Counting Homomorphisms to Sparse Graphs

Jaroslav Nesetril (1) , Patrice Ossona de Mendez (2)

1 KAM - Department of Applied Mathematics (KAM)
2 CAMS - Centre d'Analyse et de Mathématique sociales

We define nowhere dense and somewhere dense classes by means of counting of homomorphisms from test graphs. This seems to be bridging the gap between existential and counting theorems (for graph homomorphisms) and it has application to complexity of Boolean queries

Domaines: Combinatoire [math.CO]

Jaroslav Nesetril, Patrice Ossona de Mendez. Counting Homomorphisms to Sparse Graphs. European Conference on Combinatorics, Graph Theory and Applications (EuroComb 2009), Sep 2009, Bordeaux, France. pp.393-397, ⟨10.1016/j.endm.2009.07.065⟩. ⟨hal-00429958⟩