Exactly 𝑘-to-1 maps between graphs

Heath, Jo; Hilton, A. J. W.

doi:10.1090/S0002-9947-1992-1043859-X

Exactly $k$-to-$1$ maps between graphs
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by Jo Heath and A. J. W. Hilton PDF

Trans. Amer. Math. Soc. 331 (1992), 771-785 Request permission

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

Paul W. Gilbert, $n$-to-one mappings of linear graphs, Duke Math. J. 9 (1942), 475–486. MR 7106
O. G. Harrold Jr., The non-existence of a certain type of continuous transformation, Duke Math. J. 5 (1939), 789–793. MR 1358
O. G. Harrold Jr., Exactly $(k,1)$ transformations on connected linear graphs, Amer. J. Math. 62 (1940), 823–834. MR 2554, DOI 10.2307/2371492
Jo Heath and A. J. W. Hilton, Trees that admit $3$-to-$1$ maps onto the circle, J. Graph Theory 14 (1990), no. 3, 311–320. MR 1060859, DOI 10.1002/jgt.3190140304
Jo W. Heath, $K$-to-$1$ functions on arcs for $K$ even, Proc. Amer. Math. Soc. 101 (1987), no. 2, 387–391. MR 902560, DOI 10.1090/S0002-9939-1987-0902560-4
Jo Heath, $k$-to-$1$ functions between graphs with finitely many discontinuities, Proc. Amer. Math. Soc. 103 (1988), no. 2, 661–666. MR 943101, DOI 10.1090/S0002-9939-1988-0943101-6