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- W4307927042 abstract "The famous Gallai's Conjecture states that any connected graph with n vertices has a path decomposition containing at most (n+1)/2 paths. In this note, we explore graphs generated from removing edges from complete graphs. We first provide an explicit construction for a path decomposition of complete graphs that satisfies Gallai's Conjecture. We then use that construction to prove that we can remove stars and certain tadpoles such that the resulting graph still satisfies Gallai's Conjecture. We also introduce a potential general approach through analyzing non-isomorphic path decompositions of complete graphs." @default.
- W4307927042 created "2022-11-06" @default.
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- W4307927042 date "2022-10-28" @default.
- W4307927042 modified "2023-10-17" @default.
- W4307927042 title "Gallai's Conjecture for Complete and Nearly Complete Graphs" @default.
- W4307927042 doi "https://doi.org/10.48550/arxiv.2210.16406" @default.
- W4307927042 hasPublicationYear "2022" @default.
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