Trestles in the squares of graphs

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Authors

KABELA Adam TESKA Jakub

Year of publication 2021
Type Article in Periodical
Magazine / Source Discrete Mathematics
MU Faculty or unit

Faculty of Informatics

Citation
Web http://dx.doi.org/10.1016/j.disc.2021.112532
Doi http://dx.doi.org/10.1016/j.disc.2021.112532
Keywords Squares of graphs; Hamiltonicity; Trestles; Forbidden subgraphs
Description We show that the square of every connected -free graph satisfying a matching condition has a 2-connected spanning subgraph of maximum degree at most 3. Furthermore, we characterise trees whose square has a 2-connected spanning subgraph of maximum degree at most k. This generalises the results on -free graphs of Henry and Vogler [7] and Harary and Schwenk [6], respectively.
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