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Induced path factors of regular graphs

Akbari, S ; Sharif University of Technology | 2021

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  1. Type of Document: Article
  2. DOI: 10.1002/jgt.22654
  3. Publisher: John Wiley and Sons Inc , 2021
  4. Abstract:
  5. An induced path factor of a graph (Formula presented.) is a set of induced paths in (Formula presented.) with the property that every vertex of (Formula presented.) is in exactly one of the paths. The induced path number (Formula presented.) of (Formula presented.) is the minimum number of paths in an induced path factor of (Formula presented.). We show that if (Formula presented.) is a connected cubic graph on (Formula presented.) vertices, then (Formula presented.). Fix an integer (Formula presented.). For each (Formula presented.), define (Formula presented.) to be the maximum value of (Formula presented.) over all connected (Formula presented.) -regular graphs (Formula presented.) on (Formula presented.) vertices. As (Formula presented.) with (Formula presented.) even, we show that (Formula presented.) exists. We prove that (Formula presented.) and (Formula presented.) and that (Formula presented.) for (Formula presented.). © 2020 Wiley Periodicals LLC
  6. Keywords:
  7. Cubic graph ; Induced paths ; Regular graphs ; Graph theory
  8. Source: Journal of Graph Theory ; Volume 97, Issue 2 , 2021 , Pages 260-280 ; 03649024 (ISSN)
  9. URL: https://onlinelibrary.wiley.com/doi/abs/10.1002/jgt.22654