The Journal of the Indian Mathematical Society

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Chromatic Classification of Dismantlable Lattices


Affiliations
1 T. E. S's Smt. V. U. Patil Arts and Late Dr. B. S. Desale Science College, SAKRI Dist. Dhule 424304, India
2 Department of Applied Science, Shri Gulabrao Deokar College of Engineering., Jalgaon 425002, India
     

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A complete classification of the class of dismantlable lattices in terms of chromatic numbers is given. In fact, it is proved that a dismantlable lattice is at most 3-chromatic and the class of 2-Chromatic dismantlable lattices is characterized by using the structure theorem for dismantlable lattices.

Keywords

Lattice, Dismantlable Lattice, Adjunct Operation, Covering Graph, Chromatic Number.
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  • Chromatic Classification of Dismantlable Lattices

Abstract Views: 353  |  PDF Views: 1

Authors

Madhukar M. Pawar
T. E. S's Smt. V. U. Patil Arts and Late Dr. B. S. Desale Science College, SAKRI Dist. Dhule 424304, India
Vandana P. Bhamre
Department of Applied Science, Shri Gulabrao Deokar College of Engineering., Jalgaon 425002, India

Abstract


A complete classification of the class of dismantlable lattices in terms of chromatic numbers is given. In fact, it is proved that a dismantlable lattice is at most 3-chromatic and the class of 2-Chromatic dismantlable lattices is characterized by using the structure theorem for dismantlable lattices.

Keywords


Lattice, Dismantlable Lattice, Adjunct Operation, Covering Graph, Chromatic Number.

References