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 

Pages (fromto)  260280 
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

Edge decomposition of dense graphs
Australian Research Council (ARC)
30/06/17 → 31/10/22
Project: Research

Matchings in Combinatorial Structures
Wanless, I., Bryant, D. & Horsley, D.
Australian Research Council (ARC), Monash University, University of Queensland , University of Melbourne
1/01/15 → 10/10/20
Project: Research