WALCOM 2015: WALCOM: Algorithms and Computation pp 161-174

# Enumerating Eulerian Trails via Hamiltonian Path Enumeration

• Shuhei Denzumi
• Yuma Inoue
• Hiroshi Aoki
• Norihito Yasuda
• Shogo Takeuchi
• Shin-ichi Minato
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8973)

## Abstract

Given an undirected graph G, we consider enumerating all Eulerian trails, that is, walks containing each of the edges in G just once. We consider achieving it with the enumeration of Hamiltonian paths with the zero-suppressed decision diagram (ZDD), a data structure that can efficiently store a family of sets satisfying given conditions. First we compute the line graph L(G), the graph representing adjacency of the edges in G. We also formulated the condition when a Hamiltonian path in L(G) corresponds to an Eulerian trail in G because every trail in G corresponds to a path in L(G) but the converse is not true. Then we enumerate all Hamiltonian paths in L(G) satisfying the condition with ZDD by representing them as their sets of edges.

## Keywords

Eulerian trail Hamiltonian path path enumeration line graph zero-suppressed binary decision diagram

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© Springer International Publishing Switzerland 2015

## Authors and Affiliations

• 1
• Shuhei Denzumi
• 2
• Yuma Inoue
• 2
• Hiroshi Aoki
• 2
• Norihito Yasuda
• 1
• Shogo Takeuchi
• 1
• Shin-ichi Minato
• 1
• 2
1. 1.ERATO Minato Discrete Structure Manipulation System ProjectJapan Science and Technology AgencySapporoJapan
2. 2.Graduate School of Information Science and TechnologyHokkaido UniversitySapporoJapan