Nonseparating Induced Cycles Consisting of Contractible Edges in k-Connected Graphs |
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| Affiliation: | 1. Department of Applied Mathematics, Science University of Tokyo, 1-3 Kagurazaka, Shinjuku-ku, Tokyo, 162-8601, Japan;2. Department of Mathematics Faculty of Science and Technology, Keio University 3- 14- 1, Hiyoshi, Kohoku-ku, Yokohama 223-8522, Japan;1. TEMA – Centre for Mechanical Technology and Automation, Department of Mechanical Engineering, University of Aveiro, Campus de Santiago, 3810-193 Aveiro, Portugal;2. ID+ – Instituto de Investigação em Design, Media e Cultura, University of Aveiro, Campus de Santiago, 3810-193 Aveiro, Portugal;1. Department of Pathology and Laboratory Medicine, Children''s Hospital Los Angeles, Los Angeles, CA;2. Keck School of Medicine, University of Southern California, Los Angeles, CA;3. Department of Global Pediatric Medicine, Saint Jude Children''s Research Hospital, Memphis, TN;4. Aflac Cancer and Blood Disorders Center, Children''s Healthcare of Atlanta, Atlanta, GA;5. Department of Pediatrics, Emory University, Atlanta, GA;6. Department of Biostatistics, University of Florida, Gainesville, FL;7. Department of Pediatrics, University of Rochester, Rochester, NY;8. Pediatric Hematology/Oncology, Baylor College of Medicine/Dan L Duncan Comprehensive Cancer Center, Houston, TX;9. ImmunoGen Inc, Waltham, MA;10. Pediatric Hematology and Oncology, UT Southwestern/Simmons Cancer Center-Dallas, Dallas, TX;11. Department of Pathology, Johns Hopkins University/Sidney Kimmel Cancer Center, Baltimore, MD;12. Department of Pediatrics and Pathology, Laura and Isaac Perlmutter Cancer Center at NYU Langone Health, Hassenfeld Children''s Center, New York, NY;13. Division of Pediatric Hematology and Oncology, Department of Pediatrics, Laura and Isaac Perlmutter Cancer Center at NYU Langone Health, New York, NY;14. Ben Towne Center for Childhood Cancer Research, Seattle Children’s Research Institute, Seattle, WA;15. Department of Pediatrics, Seattle Children’s Hospital, University of Washington, Seattle, WA;16. Department of Pediatrics and the Center for Childhood Cancer Research, Children''s Hospital of Philadelphia, and the Perelman School of Medicine at the University of Pennsylvania, Philadelphia, PA;17. Department of Pediatrics, University of Virginia School of Medicine, Charlottesville, VA;18. Cancer and Blood Disorders Program, Children’s Minnesota, Minneapolis, MN |
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| Abstract: | It is proved that if G is a k-connected graph which does not contain K4−, then G has an induced cycle C such that G – V(C) is (k − 2)-connected and either every edge of C is k-contractible or C is a triangle. This theorem is a generalization of some known theorems. |
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