Andrea Muñoz Jiménez - Academia.edu (original) (raw)
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Graduate Center of the City University of New York
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Papers by Andrea Muñoz Jiménez
Graphs and Combinatorics, 2016
Electronic Notes in Discrete Mathematics, Dec 1, 2015
Tibor Gallai conjectured that the edge set of every connected graph G on n vertices can be partit... more Tibor Gallai conjectured that the edge set of every connected graph G on n vertices can be partitioned into ⌈n/2⌉ paths. Let G k be the class of all 2k-regular graphs of girth at least 2k − 2 that admit a pair of disjoint perfect matchings. In this work, we show that Gallai's conjecture holds in G k , for every k ≥ 3. Further, we prove that for every graph G in G k on n vertices, there exists a partition of its edge set into n/2 paths of lengths in {2k − 1, 2k, 2k + 1}.
Graphs and Combinatorics, 2016
Electronic Notes in Discrete Mathematics, Dec 1, 2015
Tibor Gallai conjectured that the edge set of every connected graph G on n vertices can be partit... more Tibor Gallai conjectured that the edge set of every connected graph G on n vertices can be partitioned into ⌈n/2⌉ paths. Let G k be the class of all 2k-regular graphs of girth at least 2k − 2 that admit a pair of disjoint perfect matchings. In this work, we show that Gallai's conjecture holds in G k , for every k ≥ 3. Further, we prove that for every graph G in G k on n vertices, there exists a partition of its edge set into n/2 paths of lengths in {2k − 1, 2k, 2k + 1}.