# eseq: Construct eulerian paths on the complete graph where nodes... In PairViz: Visualization using Graph Traversal

## 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

 ```1 2 3 4``` ```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 a path on 1..n by appending extra edges on to the path on nodes 1..(n-2).

The function eseqa constructs paths on 1..n using an alternative algorithm. For odd n, the tour starts at 1, then takes steps of size 1,2,..m repeatedly, where m is (n-1)/2, For even n, the path constructed is formed as eseqa(n+1), followed by dropping node n+1.

The function kntour\_drop removes instances of n from the 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 a tour on nodes 1, ..n. 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

`hpaths`, `eulerian`.
 ```1 2 3``` ```require(PairViz) eseq(5) eseq(6) ```