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Closed trail decompositions on grid graphs

Closed trail decompositions on grid graphs AbstractLet G = G(n, m) be a rectangular solid grid graph and 𝒜(G) be a minimum length Eulerian augmentation of G. Let l0, . . ., lt ∈ ℕ such that ∑ti=0 li = |E(𝒜(G)|, where 2(n + m) ≤ li = 2ki. In this paper, we exhibit a constructive procedure providing an edge-disjoint decomposition of 𝒜 (G) into closed trails T0, . . ., Tt such that |E(Ti)| = li. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Pure Mathematics and Applications de Gruyter

Closed trail decompositions on grid graphs

Dombi, Erzsébet
Pure Mathematics and Applications , Volume 30 (2): 14 – Aug 1, 2022
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Publisher
de Gruyter
Copyright
© 2022 Erzsébet Dombi, published by Sciendo
eISSN
1788-800X
DOI
10.1515/puma-2015-0040
Publisher site
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Abstract

AbstractLet G = G(n, m) be a rectangular solid grid graph and 𝒜(G) be a minimum length Eulerian augmentation of G. Let l0, . . ., lt ∈ ℕ such that ∑ti=0 li = |E(𝒜(G)|, where 2(n + m) ≤ li = 2ki. In this paper, we exhibit a constructive procedure providing an edge-disjoint decomposition of 𝒜 (G) into closed trails T0, . . ., Tt such that |E(Ti)| = li.

Journal

Pure Mathematics and Applications – de Gruyter

Published: Aug 1, 2022

Keywords: closed trail; graph decomposition; grid graphs; 05C70; 05C85

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