# Hamilton paths with lasting separation

## TL;DR

This paper investigates the maximum size of a family of Hamilton paths in a complete graph such that each pair of paths has a uniquely contained subpath of length k, revealing asymptotic behavior.

## Contribution

It provides the asymptotic determination of the largest family of Hamilton paths with a specific separation property in complete graphs.

## Key findings

- Asymptotic formula for the maximum size of such Hamilton path families.
- Characterization of the separation condition for pairs of paths.
- Extension of combinatorial methods to Hamilton path configurations.

## Abstract

We determine the asymptotics of the largest cardinality of a set of Hamilton paths in the complete graph with vertex set [n] under the condition that for any two of the paths in the family there is a subpath of length k entirely contained in only one of them and edge{disjoint from the other one.