Let the vertices of a circle graph be divided into several groups. This paper contains lower bounds on the size of an independent set that can be contained in one group of this subdivision. Bibliography: 7 titles.
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F. Gavril, “Algorithms for a maximum clique and a maximum independent set of a circle graph,” Networks, 3, 261–273 (1975).
H. de Fraysseix, “A characterization of circle graphs,” Europ. J. Combinatorics, 5, 223–238 (1984).
A. V. Kostochka and J. Kratochvil, “Covering and coloring polygon-circle graphs,” Disc. Math., 163, 299–305 (1997).
A. V. Kostochka, “On upper bounds for the chromatic numbers of graphs,” Trudy Inst. Math., 10, 204–226 (1988).
A. A. Ageev. “A triangle-free circle graph with chromatic number 5,” Disc. Math., 152, Nos. 1–3, 295–298 (1996).
G. V. Nenashev, “An upper bound on the chromatic number of circle graphs without K 4,” Zap. Nauchn. Semin. POMI, 391, 149–156 (2011).
V. A. Emelichev, O. I. Melnikov, V. I. Sarvanov, and R. I. Tyshkevich, Lectures in Graph Theory [in Russian], Nauka, Moscow (1990).
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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 417, 2013, pp. 5–10.
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Berlov, S.L. Independent Sets and Chromatic Numbers of Circle Graphs. J Math Sci 204, 181–184 (2015). https://doi.org/10.1007/s10958-014-2196-1
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DOI: https://doi.org/10.1007/s10958-014-2196-1