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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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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