Exactly -to- maps between graphs

Authors:
Jo Heath and A. J. W. Hilton

Journal:
Trans. Amer. Math. Soc. **331** (1992), 771-785

MSC:
Primary 05C10

MathSciNet review:
1043859

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Abstract | References | Similar Articles | Additional Information

Abstract: Suppose is a positive integer, and are graphs, and is a correspondence from a vertex set of onto a vertex set of . Conditions on the adjacency matrices are given that are necessary and sufficient for to extend to a continuous map from onto .

**[1]**Paul W. Gilbert,*𝑛-to-one mappings of linear graphs*, Duke Math. J.**9**(1942), 475–486. MR**0007106****[2]**O. G. Harrold Jr.,*The non-existence of a certain type of continuous transformation*, Duke Math. J.**5**(1939), 789–793. MR**0001358****[3]**O. G. Harrold Jr.,*Exactly (𝑘,1) transformations on connected linear graphs*, Amer. J. Math.**62**(1940), 823–834. MR**0002554****[4]**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**, 10.1002/jgt.3190140304**[5]**Jo W. Heath,*𝐾-to-1 functions on arcs for 𝐾 even*, Proc. Amer. Math. Soc.**101**(1987), no. 2, 387–391. MR**902560**, 10.1090/S0002-9939-1987-0902560-4**[6]**Jo Heath,*𝑘-to-1 functions between graphs with finitely many discontinuities*, Proc. Amer. Math. Soc.**103**(1988), no. 2, 661–666. MR**943101**, 10.1090/S0002-9939-1988-0943101-6

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Additional Information

DOI:
http://dx.doi.org/10.1090/S0002-9947-1992-1043859-X

Keywords:
Graph,
function,
map

Article copyright:
© Copyright 1992
American Mathematical Society