# Noon lecture

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On 11.12.2008 at 12:20 in S8, there is the following noon lecture:

# The complexity of the list homomorphism problem for graphs

## Benoit Larose

## Concordia University, Montreal

## Abstract

(joint work with L. Egri (McGill), A. Krokhin (Durham), P. Tesson (Laval))

We completely characterise the complexity of the list homomorphism problem for graphs in combinatorial and algebraic terms: for every graph $H$ the problem is either NP-complete, NL-complete, L-complete or has finite duality. The central result is an inductive definition of graphs whose problem is solvable in Logspace; a characterisation by forbidden subgraphs is given as well. In particular, the reflexive graphs whose list homomorphism is in Logspace are the trivially perfect graphs, or equivalently the $(P_4,C_4)$-free graphs. In the irreflexive case an analogous result is obtained: those with a list-hom problem in Logspace are the bipartite $(P_6,C_6)$-free graphs.

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