eseq {PairViz}R Documentation

Construct eulerian paths on the complete graph where nodes are integers 1..n.

Description

Constructs an eulerian on the complete graph where nodes are integers 1..n. The result in an euler tour for odd n. For even n the result is not exactly an euler tour or path because (n-2)/2 edges must be visited twice.

Usage

eseq(n)
eseqa(n)
kntour_drop(e)
kntour_add(e)

Arguments

n a positive integer.
e an euler tour on Kn where n is odd.

Details

The algorithm used for eseq builds up an euler tour on 1..n by appending extra edges on to the tour on 1..(n-2).

The function eseqa constructs tours on 1..n using an alternative algorithm.

The function kntour_drop removes instances of n from the euler tour, creating an open approximately eulerian path on the complete graph with n-1 nodes.

The function kntour_add inserts an extra node n+1 into an euler tour on the complete graph on n nodes. It adds a detour to the tour visiting all edges joining nodes 1..n to n+1. The result is an open approximately eulerian path on the complete graph with n+1 nodes.

Value

a numeric vector.

Author(s)

C.B. Hurley and R.W. Oldford

References

see overview

See Also

hpaths, eulerian.

Examples


require(PairViz)
eseq(5)
eseq(6)


[Package PairViz version 1.0 Index]