Projects per year
Abstract
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.).
Original language | English |
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Pages (from-to) | 260-280 |
Number of pages | 21 |
Journal | Journal of Graph Theory |
Volume | 97 |
Issue number | 2 |
DOIs | |
Publication status | Published - Jun 2021 |
Keywords
- covering
- induced path
- path factor
- regular graph
- subcubic graph
Projects
- 2 Finished
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Edge decomposition of dense graphs
Horsley, D. (Primary Chief Investigator (PCI))
Australian Research Council (ARC)
30/06/17 → 31/10/22
Project: Research
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Matchings in Combinatorial Structures
Wanless, I. (Primary Chief Investigator (PCI)), Bryant, D. (Chief Investigator (CI)) & Horsley, D. (Chief Investigator (CI))
Australian Research Council (ARC), Monash University, University of Queensland , University of Melbourne
1/01/15 → 10/10/20
Project: Research