Abstract
A total coloring of a graph G is to color all vertices and edges of G so that no two adjacent or incident elements receive the same color. Let C be a set of colors, and let ω be a cost function which assigns to each color c in C a real number ω(c) as a cost of c. A total coloring f of G is called an optimal total coloring if the sum of costs ω(f(x)) of colors f(x) assigned to all vertices and edges x is as small as possible. In this paper, we give an algorithm to find an optimal total coloring of any tree T in time O(nΔ3) where n is the number of vertices in T and Δ is the maximum degree of T.
Original language | English |
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Pages (from-to) | 337-342 |
Number of pages | 6 |
Journal | IEICE Transactions on Information and Systems |
Volume | E87-D |
Issue number | 2 |
Publication status | Published - 2004 Feb |
Keywords
- Cost total coloring
- Dynamic programming
- Matching
- Total coloring
- Tree
ASJC Scopus subject areas
- Software
- Hardware and Architecture
- Computer Vision and Pattern Recognition
- Electrical and Electronic Engineering
- Artificial Intelligence