A path cover of a tree T is a collection of induced paths of T that are vertex disjoint and cover all the vertices of T. A minimum path cover (MPC) of T is a path cover with the minimum possible number of paths, and that minimum number is called the path cover number of T. A tree can have just one or several MPC's.
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Consider a collection of disjoint paths in graph G such that every vertex is on one of these paths. The size of the smallest such collection is denoted i(G) ...
Consider a collection of disjoint paths in graph G such that every vertex is on one of these paths. The size of the smallest such collection is denoted i(G) ...
By replacing edges by vertices or vice versa, one can go back or forth between a minimum cover by a set of edges and a minimum cover by a set of edges and ...
Maximum edge cover by paths defined by 3 vertices in a tree
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Mar 17, 2024 · The set is maximal when the paths created by these vertices represent a tree's diameter and its longest branch.
Apr 9, 2021 · An idea behind trying to find the smallest path covering is to identify the cycles and paths. Then, start by marking each node at those cycles.
Abstract: A simple path cover of a graph G is a collection ψ of paths in G such that every edge of G is in exactly one path in ψ and any two paths in ψ have ...
AbstractConsider a collection of disjoint paths in graph G such that every vertex is on one of these paths. The size of the smallest such collection is de.
Aug 31, 2013 · There are [at least] three algorithms which find minimum vertex cover in a tree in linear (O(n)) time. What I'm interested in is a modification of all of these ...
A path cover is a set of directed paths such that every vertex v ∈ V belongs to at least one path. Note that a path cover may include paths of length 0 (a ...