# eseq

0th

Percentile

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

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.

Keywords
graphs
##### 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 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.

##### References

see overview

hpaths, eulerian.

• eseq
• eseqa
• kntour_drop
##### Examples
# NOT RUN {
require(PairViz)
eseq(5)
eseq(6)

# }

Documentation reproduced from package PairViz, version 1.3.2, License: GPL-2

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