Full paper in PDF:
$%M. Mulazzani, A “universal” class of 4-colored graphs, Rev. Mat. Univ. Complut. Madrid 9 (1996), no. 1, 165195.%$

A “Universal” Class of 4-Colored Graphs
Dipartimento di Matemática
Università di Bologna
Piazza di Porta San Donato 5
40127 Bologna Italy

Received: May 13, 1994
Revised: February 27, 1995

A family of 4-colored graphs depending on three integers b  , l  , t  , and on a transitive pair of permutations s  , t  (-  Sb  is constructed. Each associated topological space turns out to be a b  -fold branched covering of either a h  - or a handcuff-graph, with embedding depending on l  and t  , or a two-bridge knot or link of type (l,t)  . Moreover, the monodromy map is completely defined by s  and t  . In particular, when l = 2  and t= 1  , the space is homeomorphic to the (possibly singular) manifold N(s,t)  , which is the branched covering of the Montesinos universal graph, associated to the pair s  , t  . This allows us to obtain a “universal” class of 4-colored graphs representing all orientable 3-dimensional singular manifolds. Further, the necessary and sufficient condition for the graph to represent a manifold is obtained and a topological interpretation of a similar construction of A. Cavicchioli is given.

1991 Mathematics Subject Classification: Primary 57M25, 57M12; Secondary 5715.