Abstract. Given an undirected graph, a star partition is a partition of the nodes into subsets with at least two nodes so that the subgraph induced by each subset has a spanning star. Star partitions are related to well-known problems concerning domination in graphs and edge covering.
Given an undirected graph, a star partition is a partition of the nodes into subsets with at least two nodes so that the subgraph induced by each subset has a ...
People also ask
What do stars mean on a graph?
What is a partition in a graph?
What is the star decomposition of a graph?
What is a star graph in graph theory?
For every s ≥ 2, Star Partition is NP-hard on bipartite graphs [6]. Partitioning into triangles, that is, K3-Partition, is polynomial-time solvable on chordal.
Jan 14, 2024 · A partition of the vertex set of a graph G into k sets is called a star partition of G of size k if each set in the partition induces a star.
Feb 11, 2014 · We study the partitioning of undirected graphs into same-size stars, a problem known to be NP-complete even for the case of stars on three vertices.
Let G be a graph and n ≥ 2 an integer. We prove that the following are equivalent: (i) there is a partition (V1,…,Vm) of V (G) such that each Vi induces one ...
Feb 15, 2024 · In this paper, we obtain exact O ( n 2 ) time algorithms for both Star Cover and Star Partition on ( C 4 , P 4 ) -free graphs and on -free graphs.
Oct 22, 2024 · Star partitions are related to well-known problems concerning domination in graphs and edge covering. We focus on the Constrained Star Partition ...
Both STAR COVER and STAR PARTITION are NP-hard in general. In this thesis, we obtain several structural, algorithmic and hardness results for both the problems ...
We study the partitioning of undirected graphs into stars, a problem known to be NP-complete even for the case of stars on three vertices.