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Artykuł dostępny w postaci pełnego tekstu - kliknij by otworzyć plik
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Analysis of the efficiency of graph coloring algorithms

100%
Kubale M.
Mathematica Applicanda
|
1982
|
tom 10
|
nr 19
PL
.
EN
This paper discusses the computational efficiency and the number of colors used by the following algorithms for coloring vertices of graphs: sequential coloring and sequential coloring with interchange algorithms for a largest-first and a smallest-last orderings of vertices, the coloring-pairs algorithm, and the approximately maximum independent set algorithm. Each algorithm is supplied with a Pascal-like program, time complexity in terms of the size of a graph, and worst-case behaviour. In conclusion, some computational results are included with support the estimations and suggest the sequential coloring with interchange algorithm for a largest-first vertex ordering as a method which uses the least number of colors for uniformly distributed random graphs.
2
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Efficient list cost coloring of vertices and/or edges of bounded cyclicity graphs

63%
Giaro K., Kubale M.
Discussiones Mathematicae Graph Theory
|
2009
|
tom 29
|
nr 2
361-376
EN
We consider a list cost coloring of vertices and edges in the model of vertex, edge, total and pseudototal coloring of graphs. We use a dynamic programming approach to derive polynomial-time algorithms for solving the above problems for trees. Then we generalize this approach to arbitrary graphs with bounded cyclomatic numbers and to their multicolorings.
3
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Equitable Colorings Of Corona Multiproducts Of Graphs

51%
Furmánczyk H., Kubale M., Mkrtchyan V. V.
Discussiones Mathematicae Graph Theory
|
2017
|
tom 37
|
nr 4
1079-1094
EN
A graph is equitably k-colorable if its vertices can be partitioned into k independent sets in such a way that the numbers of vertices in any two sets differ by at most one. The smallest k for which such a coloring exists is known as the equitable chromatic number of G and denoted by 𝜒=(G). It is known that the problem of computation of 𝜒=(G) is NP-hard in general and remains so for corona graphs. In this paper we consider the same model of coloring in the case of corona multiproducts of graphs. In particular, we obtain some results regarding the equitable chromatic number for the l-corona product G ◦l H, where G is an equitably 3- or 4-colorable graph and H is an r-partite graph, a cycle or a complete graph. Our proofs are mostly constructive in that they lead to polynomial algorithms for equitable coloring of such graph products provided that there is given an equitable coloring of G. Moreover, we confirm the Equitable Coloring Conjecture for corona products of such graphs. This paper extends the results from [H. Furmánczyk, K. Kaliraj, M. Kubale and V.J. Vivin, Equitable coloring of corona products of graphs, Adv. Appl. Discrete Math. 11 (2013) 103–120].
4
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A new optimal algorithm for a time-dependent scheduling problem

38%
Kubale M., Ocetkiewicz K. M.
Control and Cybernetics
|
2009
|
tom 38
|
nr 3
713-721
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