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Title: Continuous k-to-1 functions between complete graphs of even order
Authors: Dugdale, J. Keith
Fiorini, Stanley
Hilton, Anthony J.W.
Gauci, John Baptist
Keywords: Complete graphs
Functions, Continuous
Graph theory -- Data processing
Graphic methods -- Data processing
Issue Date: 2010
Publisher: Elsevier BV. North-Holland
Citation: Dugdale, J. K., Fiorini, S., Hilton, A. J., & Gauci, J. B. (2010). Continuous k-to-1 functions between complete graphs of even order. Discrete Mathematics, 310(2), 330-346.
Abstract: A function between graphs is k-to-1 if each point in the co-domain has precisely k pre-images in the domain. Given two graphs, G and H, and an integer k ≥ 1, and considering G and H as subsets of R 3, there may or may not be a k-to-1 continuous function (i.e. a k-to-1 map in the usual topological sense) from G onto H. In this paper we review and complete the determination of whether there are finitely discontinuous, or just infinitely discontinuous k-to-1 functions between two intervals, each of which is one of the following: ]0, 1[, [0, 1[and [0, 1]. We also show that for k even and 1 ≤ r < 2s, (r, s) 6= (1, 1) and (r, s) 6= (3, 2), there is a k-to-1 map from K2r onto K2s if and only if k ≥ 2s.
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