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Chromatic uniqueness of elements of height ≤ 3 in lattices of complete multipartite graphs

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Abstract

For integers n and t such that 0 < t < n and a nonnegative integer h ≤ 3, it is proved that any complete t-partite n-graph with nontrivial parts and height h in the lattice NPL(n, t) of partitions of the positive integer n into t additive terms is chromatically unique.

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References

  1. T. A. Sen’chonok and V. A. Baranskii, Trudy Inst. Mat. Mekh. UrO RAN 17(2), 159 (2011).

    Google Scholar 

  2. T. A. Sen’chonok, Trudy Inst. Mat. Mekh. UrO RAN 17(3), 271 (2011).

    Google Scholar 

  3. G. Andrews, The Theory of Partitions (Addison-Wesley, London, 1976; Nauka, Moscow, 1982).

    MATH  Google Scholar 

  4. V. A. Baranskii and T. A. Koroleva, Dokl. Math. 77(1), 72 (2008).

    Article  MathSciNet  Google Scholar 

  5. R. C. Read, J. Comb. Theory 4, 52 (1968).

    Article  MathSciNet  Google Scholar 

  6. C. Y. Chao and E. G. Whitehead, Jr., Theory Appl. Graphs 642, 121 (1978).

    Article  MathSciNet  Google Scholar 

  7. H. Zhao, Chromaticity and Adjoint Polynomials of Graphs (Wöhrmann, Zutphen, 2005).

    Google Scholar 

  8. C. Y. Chao and G. A. Novacky, Jr., Discrete Math. 41, 139 (1982).

    Article  MathSciNet  MATH  Google Scholar 

  9. V. A. Baranskii and T. A. Koroleva, Proc. Steklov Inst. Math., Suppl. 1, S15 (2008).

  10. T. A. Koroleva, Trudy Inst. Mat. Mekh. UrO RAN 13(3), 65 (2007).

    MathSciNet  Google Scholar 

  11. T. A. Koroleva, Izv. Ural’sk. Gos. Univ. 74, 39 (2010).

    MathSciNet  Google Scholar 

  12. V. A. Baranskii and T. A. Koroleva, Izv. Ural’sk. Gos. Univ. 74, 5 (2010).

    MathSciNet  Google Scholar 

  13. K. M. Koh and K. L. Teo, Graphs Combin. 6, 259 (1990).

    Article  MathSciNet  MATH  Google Scholar 

  14. E. J. Farrell, Discrete Math. 29, 257 (1980).

    Article  MathSciNet  MATH  Google Scholar 

  15. V. A. Baranskii and S. V. Vikharev, Izv. Ural’sk. Gos. Univ. 36, 25 (2005).

    MathSciNet  Google Scholar 

  16. M. O. Asanov, V. A. Baranskii, and V. V. Rasin, Discrete Mathematics: Graphs, Matroids, Algorithms (Lan’, St.-Petersburg, 2010) [in Russian].

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Authors and Affiliations

  1. Institute of Mathematics and Computer Science, Ural Federal University, pr. Lenina 51, Yekaterinburg, 620083, Russia

    V. A. Baranskii & T. A. Sen’chonok

Authors
  1. V. A. Baranskii
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  2. T. A. Sen’chonok
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Correspondence to V. A. Baranskii.

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Original Russian Text © V.A. Baranskii, T.A. Sen’chonok, 2011, published in Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2011, Vol. 17, No. 4.

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Baranskii, V.A., Sen’chonok, T.A. Chromatic uniqueness of elements of height ≤ 3 in lattices of complete multipartite graphs. Proc. Steklov Inst. Math. 279 (Suppl 1), 1–16 (2012). https://doi.org/10.1134/S0081543812090015

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  • DOI: https://doi.org/10.1134/S0081543812090015

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