Work

Enumerating Hamiltonian Paths and Cycles

Year: 2026

Type: preprint

Abstract: We prove counting formulae for the number of directed Hamiltonian paths and directed Hamiltonian cycles in any complete multipartite graph. The method is based on a collapsing technique relating general path graphs with coloured vertices to legally coloured path graphs.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.06644

Authors: Hylock, Harry, Schmidt, Karl Michael, Lettington, Matthew C.

Language: English

Topic: Advanced Combinatorial Mathematics

Subfield: Discrete Mathematics and Combinatorics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W7220709990

Cites: 1

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Related to: 10