Finite duality for some minor closed classes Jaroslav Neˇ setˇ ril 1,2 Department of Applied Mathematics, Institute for Theoretical Computer Science(ITI) Charles University Prague, Czech Republic Yared Nigussie 3 Department of Mathematics East Tennessee State University Jhonson City, USA Abstract Let K be a class of finite graphs and F = {F 1 ,F 2 , ..., F m } be a set of finite graphs. Then, K is said to have finite-duality if there exists a graph U in K such that for any graph G in K, G is homomorphic to U if and only if F i is not homomorphic to G, for all i =1, 2, ..., m. Neˇ setˇ ril asked in [5] if non-trivial examples can be found. In this note, we answer this positively by showing classes containing arbitrary long anti-chains and yet having the finite-duality property. Keywords: Finite duality, homomorphism, minor 1 Supported by a Grant 1M002160808 of Czech Ministry of Education 2 Email: nesetril@kam.mff.cuni.cz 3 Email: nigussie@etsu.edu Electronic Notes in Discrete Mathematics 29 (2007) 579–585 1571-0653/$ – see front matter © 2007 Published by Elsevier B.V. www.elsevier.com/locate/endm doi:10.1016/j.endm.2007.07.092