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H-Colorings of Large Degree Graphs

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EurAsia-ICT 2002: Information and Communication Technology (EurAsia-ICT 2002)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2510))

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Abstract

We consider the H-coloring problem on graphs with vertices of large degree. We prove that for H an odd cycle, the problem belongs to P. We also study the phase transition of the problem, for an infinite family of graphs of a given chromatic number, i.e. the threshold density value for which the problem changes from P to NP-complete. We extend the result for the case that the input graph has a logarithmic size of small degree vertices. As a corollary, we get a new result on the chromatic number; a new family of graphs, for which computing the chromatic number can be done in polynomial time.

This research was supported by the IST Program of the EU under contract number IST-99-14186 (ALCOM-FT) and the Spanish CICYT project TIC2000-1970-CE. The second author was also supported by the Czech Ministry of Education project LN00A056 and the forth author was further supported by the Ministry of Education and Culture of Spain (Resolución 31/7/00 - BOE 16/8/00).

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References

  1. R. J. Anderson and E. W. Mayr. Approximating P-complete problems. Technical report, Stanford University, 1986.

    Google Scholar 

  2. B. Bollobás: Modern Graph Theory, Springer 1998.

    Google Scholar 

  3. K. Edwards. The complexity of colouring problems on dense graphs. Theoretical Computer Science, 43:337–343, 1986.

    Article  MATH  MathSciNet  Google Scholar 

  4. P. Erdös. On the structure of linear graphs. Israel Journal of Mathematics, 1:156–160, 1963.

    Article  MATH  MathSciNet  Google Scholar 

  5. P. Hell and J. Nešetřil. On the complexity of H-coloring. Journal of Combinatorial Theory, series B, 48:92–110, 1990.

    Article  MATH  MathSciNet  Google Scholar 

  6. F. S. Roberts: T-colorings of Graphs Recent Results and Open Problems, Discrete Math. 93(1991), 229–245

    Article  MathSciNet  MATH  Google Scholar 

  7. X. Zhu. Circular chromatic number: A survey. In: Combinatorics, Graph Theory, Algorithms and Applications-DIMATIA Survey Collection (M. Fiedler, J. Kratochvíl, J. Nešetřil, eds.), North Holland (2000)

    Google Scholar 

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© 2002 Springer-Verlag Berlin Heidelberg

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Díaz, J., Nešetřil, J., Serna, M., Thilikos, D.M. (2002). H-Colorings of Large Degree Graphs. In: Shafazand, H., Tjoa, A.M. (eds) EurAsia-ICT 2002: Information and Communication Technology. EurAsia-ICT 2002. Lecture Notes in Computer Science, vol 2510. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-36087-5_98

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  • DOI: https://doi.org/10.1007/3-540-36087-5_98

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-00028-0

  • Online ISBN: 978-3-540-36087-2

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