ScienceDirect - Discrete Mathematics : The 7-cycle C7 is light in the family of planar graphs with minimum degree 5

Discrete Mathematics
Volume 307, Issues 11-12, 28 May 2007, Pages 1430-1435
The Fourth Caracow Conference on Graph Theory - Czorsztyn 2002

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doi:10.1016/j.disc.2005.11.080

The 7-cycle C₇ is light in the family of planar graphs with minimum degree 5

T. Madaras^a^,¹^,²^,, R. Škrekovski^b^,^c^,¹^,³^,^, and H.-J. Voss^d^,^,

^aInstitute of Mathematics, University of P.J. Šafárik, Jesenná 5, 041 54 Košice, Slovak Republic ^bFaculty of Mathematics and Physics, DIMATIA and Institute for Theoretical Computer Science (ITI), Charles University, Malostranské nám. 2/25, 118 00 Prague, Czech Republic ^cDepartment of Mathematics, University of Ljubljana, Jadranska 19, 1111 Ljubljana, Slovenia ^dDepartment of Mathematics, Technical University of Dresden, D-01062 Dresden, Germany

Received 3 October 2002;

revised 27 June 2003;

accepted 18 November 2005.

Available online 5 December 2006.

References and further reading may be available for this article. To view references and further reading you must purchase this article.

Abstract

A connected graph H is said to be light in the family of graphs if there exists a positive integer k such that each graph that contains an isomorphic copy of H contains a subgraph K isomorphic to H that satisfies the inequality . It is known that an r-cycle C_r is light in the family of planar graphs with minimum degree 5 if 3r6, and not light for r11. We prove that C₇ is also light in this family.