article · 1999
HOMOMORPHISM ONTO Z
Aleksander Malnič, Norbert Seifter, Boris Zgrablić, Aleksander Malnic, Dragan Marusic, Montanuniversitat Leoben
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Abstract
In an in nite digraph D, an edge e 0 is reachable from an edge e if there exists an alternating walk in D whose initial and terminal edges are e and e 0. Reachability is an equivalence relation and if D is 1-arc-transitive, then this relation is either universal or all of its equivalence classes induce isomorphic bipartite digraphs. In [1, Question 1.3], Cameron, Praeger and Wormald asked if there exist highly arctransitive digraphs (apart from directed cycles) for which the reachability relation is not universal and whichdonothaveahomomorphism onto the two-way in nite directed path (a Cayley digraph of Z with respect to one generator). Evans [2] gave an a rmative answer by constructing a locally in nite example. For each oddinteger n 3, a construction of a highly arc-transitive digraph without property Z satisfying the additional properties that its in- and out-degrees are equal to 2 and that the reachability equivalence classes induce alternating cycles of length 2n, is given. Furthermore, using the line digraph operator, digraphs having the above properties but with alternating cycles of length 4 are obtained.
Cite this paper
Malnič, A., Seifter, N., Zgrablić, B., Malnic, A., Marusic, D., & Leoben, M. (1999). HOMOMORPHISM ONTO Z.
Malnič, Aleksander, et al. “HOMOMORPHISM ONTO Z.” 1999.
Malnič, Aleksander, Norbert Seifter, Boris Zgrablić, Aleksander Malnic, Dragan Marusic, and Montanuniversitat Leoben. 1999. “HOMOMORPHISM ONTO Z.”
Malnič, A. et al. (1999) ‘HOMOMORPHISM ONTO Z’.
@article{malnic1999homomorphism,
title = {{HOMOMORPHISM ONTO Z}},
author = {Malnič, Aleksander and Seifter, Norbert and Zgrablić, Boris and Malnic, Aleksander and Marusic, Dragan and Leoben, Montanuniversitat},
year = {1999}
}Made from the index record. Check names, capitalisation and page numbers against the paper. Need another style? AI for Research has over 10,000.