@article{cd1bd94e81cc491fb6c498eab6b1f587,
title = "Plane curves in an immersed graph in R2",
abstract = "For any chord diagram on a circle there exists a complete graph on sufficiently many vertices such that any generic immersion of it to the plane contains a plane-closed curve whose chord diagram contains the given chord diagram as a sub-chord diagram. For any generic immersion of the complete graph on six vertices to the plane, the sum of averaged invariants of all Hamiltonian plane curves in it is congruent to one quarter modulo one-half.",
keywords = "Immersed graph, chord diagram, knot, plane curve",
author = "Marisa Sakamoto and Kouki Taniyama",
note = "Funding Information: The authors are grateful to Professors Shin{\textquoteright}ichi Suzuki and Toshie Takata for their encouragements. The authors are also grateful to Professors Toshiki Endo, Reiko Shinjo, Noboru It{\^o} and Ryo Hanaki for their helpful comments. The second author was partially supported by Grant-in-Aid for Scientific Research (C) (No. 24540100), Japan Society for the Promotion of Science.",
year = "2013",
month = feb,
doi = "10.1142/S021821651350003X",
language = "English",
volume = "22",
journal = "Journal of Knot Theory and its Ramifications",
issn = "0218-2165",
publisher = "World Scientific Publishing Co. Pte Ltd",
number = "2",
}