Coloured knots and coloured graphs representing 3-fold simple coverings of %plane1D;54A;3
نویسندگان
چکیده
منابع مشابه
Coloured Knots and Permu- Tations Representing 3-mani- Folds
It is known that every closed orientable 3-manifold can be represented by coloured knots ((4], 5]), edge-coloured graphs ((2]) or transitive permutation pairs ((6]). The present paper describes some relations between these representation theories: in particular, it is shown how to obtain a transitive permutation pair representing a 3-manifold M 3 , starting from a coloured knot representing M 3 .
متن کاملColoured Untying of Knots
For p 3 and for p 5 we show that every p-coloured knot K can be reduced to a left-hand pp, 2q-torus knot by a sequence of surgeries along components in the kernel of its p-colouring ρ : π1pS3 Kq ÝÑ D2p . This gives us a 3-colour and a 5-colour analogue of the surgery presentation of a knot in the complement of an unknot. AMS Classification 57M25; 57M10,57M27
متن کاملVertex Coverings by Coloured Induced Graphs - Frames and Umbrellas
A graph G homogeneously embeds in a graph H if for every vertex x of G and every vertex y of H there is an induced copy of G in H with x at y. The graph G uniformly embeds in H if for every vertex y of H there is an induced copy of G in H containing y. For positive integer k, let fk(G) (respectively, gk(G)) be the minimum order of a graph H whose edges can be k-coloured such that for each colou...
متن کاملSurgery untying of coloured knots
A p–colouring of a knot K is a surjective homomorphism ρ from its knot group G := π1(S − K) to D2p := {t, s|t2 = sp = 1, tst = sp−1} the dihedral group of order 2p, when p is any odd integer. The pair (K, ρ) is called a p–coloured knot. It is a well-known fact that we can encode ρ as a colouring of arcs of a knot diagram by elements of Zp (the cyclic group of order p), subject to the ‘colouring...
متن کاملHomogeneous coloured multipartite graphs
We classify the countable homogeneous coloured multipartite graphs with any finite number of parts. By Fräıssé’s Theorem this amounts to classifying the families F of pairwise non-embeddable finite coloured multipartite graphs for which the class Forb(F) of multipartite graphs which forbid these is an amalgamation class. We show that once we understand such families F in the quadripartite case,...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1995
ISSN: 0012-365X
DOI: 10.1016/0012-365x(93)e0145-t