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An Alternate method to find the chromatic number of a Finite, Connected Graph [article]

Athma. M. Ram, R. Rama
2019 arXiv   pre-print
A new algorithm to obtain the chromatic number of a finite, connected graph is proposed in this paper. The algorithm is based on contraction of non adjacent vertices.  ...  Acknowledgements The authors would like thank Dr.Sadagopan N, Department of Computer Science & Engg, IIITD&M for the valuable comments.  ...  The chromatic number of a graph is denoted as ( ). For ( ), ( ) denotes the neighborhood of vertex in graph .  ... 
arXiv:1309.3642v3 fatcat:g7ehvrv4ifcxtgwkeljxpx2ybi

Finding the chromatic number by means of critical graphs

Francine Herrmann, Alain Hertz
2002 ACM Journal of Experimental Algorithmics  
We propose a new exact algorithm for finding the chromatic number of a graph G.  ...  The algorithm attempts to determine the smallest possible induced subgraph G of G which has the same chromatic number as G.  ...  Fig. 1 . 1 A new exact algorithm for the computation of the chromatic number of a graph G. £.G© , for each vertex x G© .  ... 
doi:10.1145/944618.944628 fatcat:syw6sih63zbvdlh5rkpnmajz6m

Finding the chromatic number by means of critical graphs

Francine Herrmann, Alain Hertz
2000 Electronic Notes in Discrete Mathematics  
We propose a new exact algorithm for finding the chromatic number of a graph G.  ...  The algorithm attempts to determine the smallest possible induced subgraph G of G which has the same chromatic number as G.  ...  Fig. 1 . 1 A new exact algorithm for the computation of the chromatic number of a graph G. £.G© , for each vertex x G© .  ... 
doi:10.1016/s1571-0653(05)80155-6 fatcat:oylwxhacqng4haq52yzkkydrn4

The computation of chromatic polynomials

Gary Haggard, Thomas R. Mathies
1999 Discrete Mathematics  
The computation of the chromatic polynomial of this graph is computed by enhancing the algorithm based on the classical Delete-Contract theorem as well as finding approaches for substantially modifying  ...  The planar graph representing the truncated icosahedron is a cubic graph with 60 vertices and 90 edges.  ...  The first is to develop and implement an effective algorithm for computing the chromatic polynomial of the face map of the graph shown in Fig. 1 .  ... 
doi:10.1016/s0012-365x(98)00343-4 fatcat:2txofzddj5fjtggrygtrydgdau

Page 6042 of Mathematical Reviews Vol. , Issue 2000i [page]

2000 Mathematical Reviews  
So one defines the on-line chromatic number 7*(G) as follows: If A is an on-line colouring algorithm, then 74(G) is the maximum number of colours used by A given any ordering of the vertices, and y*(G)  ...  (b) In the ith step the algorithm assigns a proper colour to v;. The well-known greedy algorithm is an example of an on-line colouring algorithm.  ... 

OVERVIEW OF GRAPH COLORING METHODS AND ALGORITHMS

Олексій Денисенко
2019 ΛΌГOΣ. МИСТЕЦТВО НАУКОВОЇ ДУМКИ  
The purpose of the work is to analyze heuristic methods and describe computational experiments using a program for heuristic evaluation of a chromatic number.  ...  Comparison of the results of the use of different methods for graphs which differ in such properties as, for example, the number of vertices and connection density, depending on search parameters of specific  ...  Comparison of algorithms for finding chromatic number of a graph. The graph coloring problem is an NP-complete problem.  ... 
doi:10.36074/2617-7064.07.00.006 fatcat:awmcleldsjbgljepl7psofshje

Small Maximal Independent Sets and Faster Exact Graph Coloring

David Eppstein
2003 Journal of Graph Algorithms and Applications  
As a consequence, we show how to compute the exact chromatic number of a graph in time O((4/3 + 3 4/3 /4) n ) ≈ 2.4150 n , improving a previous O((1 + 3 1/3 ) n ) ≈ 2.4422 n algorithm of Lawler (1976).  ...  We show that, for any n-vertex graph G and integer parameter k, there are at most 3 4k−n 4 n−3k maximal independent sets I ⊂ G with |I| ≤ k, and that all such sets can be listed in time O(3 4k−n 4 n−3k  ...  It contains two results: an algorithm for finding a 3-coloring of a graph (if the graph is 3-chromatic) in time O(3 n/3 ) ≈ 1.4422 n , and an algorithm for finding the chromatic number of an arbitrary  ... 
doi:10.7155/jgaa.00064 fatcat:qutjj4g3rbba3hjsji7dnazejy

Small Maximal Independent Sets and Faster Exact Graph Coloring [chapter]

David Eppstein
2006 Graph Algorithms and Applications 4  
As a consequence, we show how to compute the exact chromatic number of a graph in time O((4/3 + 3 4/3 /4) n ) ≈ 2.4150 n , improving a previous O((1 + 3 1/3 ) n ) ≈ 2.4422 n algorithm of Lawler (1976).  ...  We show that, for any n-vertex graph G and integer parameter k, there are at most 3 4k−n 4 n−3k maximal independent sets I ⊂ G with |I| ≤ k, and that all such sets can be listed in time O(3 4k−n 4 n−3k  ...  It contains two results: an algorithm for finding a 3-coloring of a graph (if the graph is 3-chromatic) in time O(3 n/3 ) ≈ 1.4422 n , and an algorithm for finding the chromatic number of an arbitrary  ... 
doi:10.1142/9789812773296_0006 fatcat:ctme3hxfwrcsnbj22loviyzw3u

Graph radio coloring concepts

R. Kalfakakou, G. Nikolakopoulou, E. Savvidou, M. Tsouros
2003 Yugoslav Journal of Operations Research  
A heuristic algorithm that finds approximate values of the radio chromatic number and radio chromatic cost of a given graph is developed and the result of a computational experiment of the proposed algorithm  ...  In the present paper we give the definition of the graph radio coloring concept which is a graph coloring generalization.  ...  Section 3 is devoted to a procedure that we call algorithm A that finds a good approximation of the chromatic number and the chromatic cost respectively for an arbitrary graph.  ... 
doi:10.2298/yjor0302207k fatcat:xkit4e2xunhdrglwx6zqin33ly

Small Maximal Independent Sets and Faster Exact Graph Coloring [chapter]

David Eppstein
2001 Lecture Notes in Computer Science  
As a consequence, we show how to compute the exact chromatic number of a graph in time O((4/3 + 3 4/3 /4) n ) ≈ 2.4150 n , improving a previous O((1 + 3 1/3 ) n ) ≈ 2.4422 n algorithm of Lawler (1976).  ...  We show that, for any n-vertex graph G and integer parameter k, there are at most 3 4k−n 4 n−3k maximal independent sets I ⊂ G with |I| ≤ k, and that all such sets can be listed in time O(3 4k−n 4 n−3k  ...  It contains two results: an algorithm for finding a 3-coloring of a graph (if the graph is 3-chromatic) in time O(3 n/3 ) ≈ 1.4422 n , and an algorithm for finding the chromatic number of an arbitrary  ... 
doi:10.1007/3-540-44634-6_42 fatcat:arb7l5664jaonf2wjxsivr3kg4

Small Maximal Independent Sets and Faster Exact Graph Coloring [article]

David Eppstein
2000 arXiv   pre-print
As a consequence, we show how to compute the exact chromatic number of a graph in time O((4/3 + 3^4/3/4)^n) = 2.4150^n, improving a previous O((1+3^1/3)^n) = 2.4422^n algorithm of Lawler (1976).  ...  We show that, for any n-vertex graph G and integer parameter k, there are at most 3^4k-n4^n-3k maximal independent sets I ⊂ G with |I| <= k, and that all such sets can be listed in time O(3^4k-n 4^n-3k  ...  It contains two results: an algorithm for finding a 3-coloring of a graph (if the graph is 3-chromatic) in time O(3 n/3 ) ≈ 1.4422 n , and an algorithm for finding the chromatic number of an arbitrary  ... 
arXiv:cs/0011009v1 fatcat:tcbdf2rbvnan5k7i7x2nx5ihpm

New Algorithm for Chromatic Number of Graphs and their Applications

H. Rafat
2018 Journal of the Egyptian Mathematical Society  
In this paper, we have designed a new algorithm for calculating the exact value of the chromatic number of a graph and dubbed it as R-coloring algorithm.  ...  Using this R-coloring algorithm, we have proved some results. We have discussed some application in different fields of our life by using this new algorithm.  ...  Conclusion A new algorithm for calculating the exact value of the chromatic number of a graph has been designed and dubbed as R-coloring algorithm.  ... 
doi:10.21608/joems.2018.3353.1076 fatcat:hc664pafojghjgx3fyvhg5aswy

A local search algorithm based on chromatic classes for university course timetabling problem

Velin Kralev, Radoslava Kraleva
2016 International Journal of Advanced Computer Research  
Conflicts of interest The authors have no conflicts of interest to declare.  ...  In fact, the matrix of the conflicts is another way for a graph to be represented by an adjacency matrix.  ...  The main idea of the algorithm was through a heuristic algorithm to specify the chromatic classes of a graph in which the events of the timetable correspond to the graph vertices and the set of the edges  ... 
doi:10.19101/ijacr.2016.627011 fatcat:maods7s56jdarkqxqi4wpgls2y

An Algorithm for Optimal Acyclic Edge-Colouring of Cubic Graphs [chapter]

Edita Máčajová, Ján Mazák
2011 Lecture Notes in Computer Science  
The acyclic chromatic index of a graph G is the smallest possible number of colours in an acyclic edge-colouring of G.  ...  In [12], we have shown that the acyclic chromatic index of a connected subcubic graph G is at most 4 with the exception of K4 and K3,3, for which five colors are optimal.  ...  Similarly we define the acyclic chromatic index (also called acyclic edge chromatic number) of a graph G, denoted by a (G), to be the least integer k such that G has an acyclic k-edge-colouring.  ... 
doi:10.1007/978-3-642-21204-8_17 fatcat:bxdyxkl3ivetvm4ilkpc2tvbbu

A Computation on Any 3-Coloring Graph is a Pproblem

X.-J. Wang, T.-Q. Wang
2021 Zenodo  
In general, the coloring problem for a graph and an integer k is to determine whether its chromatic number is at most or not; the kcolorability problem is to verify whether vertices of a given graph can  ...  It is one of the open problems, whether or not the algorithm for a 3-coloring graph is in polynomial time1-3.  ...  In general, the coloring problem for a graph and an integer k is to determine whether its chromatic number is at most or not; the kcolorability problem is to verify whether vertices of a given graph can  ... 
doi:10.5281/zenodo.4748658 fatcat:icaguajkmvh55l4psy6sgxnfre
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