Induced path factors of regular graphs

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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 languageEnglish
Number of pages21
JournalJournal of Graph Theory
DOIs
Publication statusAccepted/In press - 18 Dec 2020

Keywords

  • covering
  • induced path
  • path factor
  • regular graph
  • subcubic graph

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