Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Exactly $ k$-to-$ 1$ maps between graphs


Authors: Jo Heath and A. J. W. Hilton
Journal: Trans. Amer. Math. Soc. 331 (1992), 771-785
MSC: Primary 05C10
DOI: https://doi.org/10.1090/S0002-9947-1992-1043859-X
MathSciNet review: 1043859
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Suppose $ k$ is a positive integer, $ G$ and $ H$ are graphs, and $ f$ is a $ k{\text{-to-}}1$ correspondence from a vertex set of $ G$ onto a vertex set of $ H$. Conditions on the adjacency matrices are given that are necessary and sufficient for $ f$ to extend to a continuous $ k{\text{-to-}}1$ map from $ G$ onto $ H$.


References [Enhancements On Off] (What's this?)

  • [1] P. Gilbert, $ n$-to-one mappings of linear graphs, Duke Math. J. 9 (1942), 475-486. MR 0007106 (4:88b)
  • [2] O. G. Harrold, The non-existence of a certain type of continuous transformation, Duke Math. J. 5 (1939), 789-793. MR 0001358 (1:223c)
  • [3] -, Exactly $ (k,1)$ transformations on connected linear graphs, Amer. J. Math. 62 (1940), 823-834. MR 0002554 (2:75c)
  • [4] Jo Heath and A. J. W. Hilton, Trees that admit $ 3$-to-$ 1$ maps onto the circle, J. Graph Theory 14 (1990), 311-320. MR 1060859 (91i:54008)
  • [5] Jo Heath, $ k$-to-$ 1$ functions on arcs for $ K$ even, Proc. Amer. Math. Soc. 101 (1987), 387-391. MR 902560 (89b:26002)
  • [6] -, $ k$-to-$ 1$ functions between graphs with finitely many discontinuities, Proc. Amer. Math. Soc. 103 (1988), 661-666. MR 943101 (89i:05104)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 05C10

Retrieve articles in all journals with MSC: 05C10


Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1992-1043859-X
Keywords: Graph, $ k{\text{-to-}}1$ function, $ k{\text{-to}} 1$ map
Article copyright: © Copyright 1992 American Mathematical Society

American Mathematical Society