Transforming eulerian trails

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چکیده

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Transforming eulerian trails

Fleischner, H., G. Sabidussi and E. Wenger, Transforming eulerian trails, Discrete Mathematics 109 (1992) 103-116. In this paper a set of transformations (K-transformations) between eulerian trails is investigated. It is known that two arbitrary eulerian trails can be transformed into each other by a sequence of K-transformations. For compatible eulerran trails the set of K-transformations is a...

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Enumerating Eulerian Trails Based on Line Graph Conversion

(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 grap...

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Finite automata for testing uniqueness of Eulerian trails

We investigate the condition under which the Eulerian trail of a digraph is unique, and design a finite automaton to examine it. The algorithm is effective, for if the condition is violated, it will be noticed immediately without the need to trace through the whole trail.

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Crossed TRAILs

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Spanning trails

A graph is called 2K2-free if it does not contain two independent edges as an induced subgraph. Mou and Pasechnik conjectured that every 3 2 -tough 2K2-free graph with at least three vertices has a spanning trail with maximum degree at most 4. In this paper, we confirm this conjecture. We also provide examples for all t < 54 of t-tough graphs that do not have a spanning trail with maximum degre...

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ژورنال

عنوان ژورنال: Discrete Mathematics

سال: 1992

ISSN: 0012-365X

DOI: 10.1016/0012-365x(92)90281-j