- Tytuł:
- Minimum vertex ranking spanning tree problem for chordal and proper interval graphs
- Autorzy:
- Dereniowski, Dariusz
- Powiązania:
- https://bibliotekanauki.pl/articles/743173.pdf
- Data publikacji:
- 2009
- Wydawca:
- Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
- Tematy:
-
computational complexity
vertex ranking
spanning tree - Opis:
- A vertex k-ranking of a simple graph is a coloring of its vertices with k colors in such a way that each path connecting two vertices of the same color contains a vertex with a bigger color. Consider the minimum vertex ranking spanning tree (MVRST) problem where the goal is to find a spanning tree of a given graph G which has a vertex ranking using the minimal number of colors over vertex rankings of all spanning trees of G. K. Miyata et al. proved in [NP-hardness proof and an approximation algorithm for the minimum vertex ranking spanning tree problem, Discrete Appl. Math. 154 (2006) 2402-2410] that the decision problem: given a simple graph G, decide whether there exists a spanning tree T of G such that T has a vertex 4-ranking, is NP-complete. In this paper we improve this result by proving NP-hardness of finding for a given chordal graph its spanning tree having vertex 3-ranking. This bound is the best possible. On the other hand we prove that MVRST problem can be solved in linear time for proper interval graphs.
- Źródło:
-
Discussiones Mathematicae Graph Theory; 2009, 29, 2; 253-261
2083-5892 - Pojawia się w:
- Discussiones Mathematicae Graph Theory
- Dostawca treści:
- Biblioteka Nauki
Artykuł