Induced path factors of regular graphs
Saieed Akbari, Daniel Horsley, Ian M. Wanless · Journal of Graph Theory · 2020
Abstract An induced path factor of a graph is a set of induced paths in with the property that every vertex of is in exactly one of the paths. The induced path number of is the minimum number of paths in an induced path factor of . We show that if is a connected cubic graph on vertices, then . Fix an integer . For each , define to be the maximum value of over all connected ‐regular graphs on vertices. As with even, we show that exists. We prove that and and that for .