Description Usage Arguments Details Value Author(s) References See Also Examples

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.

1 2 3 4 | ```
eseq(n)
eseqa(n)
kntour_drop(e)
kntour_add(e)
``` |

`n` |
a positive integer. |

`e` |
an euler tour on Kn where n is odd |

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.

a numeric vector.

C.B. Hurley and R.W. Oldford

see overview

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