Chromatic Classification of Dismantlable Lattices

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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 ,IN
  • Vandana P. Bhamre
     Department of Applied Science, Shri Gulabrao Deokar College of Engineering., Jalgaon 425002 ,IN

Keywords:

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

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.

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Published

2016-12-01

How to Cite

Pawar, M. M., & Bhamre, V. P. (2016). Chromatic Classification of Dismantlable Lattices. The Journal of the Indian Mathematical Society, 83(3-4), 329–335. Retrieved from https://informaticsjournals.com/index.php/jims/article/view/6613

Issue

Volume 83, Issue 3-4, July-December 2016

Section

Articles

License

Copyright (c) 2016 Madhukar M. Pawar, Vandana P. Bhamre

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

 

References

B. Bollobas, Coloring lattices, Algebra Universalis, 7 (1977), 313-314.

B. Bollobas and I. Rival, The maximal size of the covering graph of a lattice, Algebra Universalis, 9 (1979), 371-373.

B. A. Davey and H. A. Priestley, Introduction to lattices and order, Cambridge University Press, 1990.

N. D. Filipov, Comparability graphs of partially ordered sets of different types, Colloq. Math. Soc. Janos Bolyai, 33 (1980), 373-380

G. Gratzer, General lattice theory , Academic press, New York, 1978.

D. Kelley, and I. Rival, Crown, fences and dismantlable lattices, Canad. J. Math. 27 (1974), 636-665.

S. K. Nimbhorkar, M. P.Wasadikar, and M.M. Pawar, Colorig of lattices, Math. Slovaca, 60(4) (2010), 419-434.

A. Patil, B. N. Waphare, V. Joshi and H. Y. Pourali, Zero divisor graphs of lower dismantlable lattices-I, Math. Slovaca, (To appear).

M. M. Pawar, Symmetricity and enumeration in posests, Ph.D. Thesis, North Maharashtra University, Jalgaon, 1999.

I. Rival, Lattices with doubly irreducible elements, Canad. Math. Bull., 17 (1974), 91-95.

N. K. Thakare, M. M. Pawar, and B. N. Waphare, A structure theorem for dismantlable lattices and enumeration, Period. Math. Hungarica 45(1-2) (2002), 147-160.

D. B. West, Introduction to Graph Theory, Pearson Education, Inc., New Jersey, 2001.