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The 2-Extendability of Graphs on the Projective Plane, the Torus and the Klein Bottle
Authors:Iwao Mizukai  Seiya Negami  Yusuke Suzuki
Affiliation:1. Graduate School of Department of Information Media and Environment Sciences, Yokohama National University, 79-7 Tokiwadai, Hodogaya-Ku, Yokohama, 240-8501, Japan
2. Faculty of Education and Human Sciences, Yokohama National University, 79-7 Tokiwadai, Hodogaya-Ku, Yokohama, 240-8501, Japan
3. Tsuruoka National College of Technology, Tsuruoka, Yamagata, 997-8511, Japan
Abstract:A graph is said to be k-extendable if any independent set of k edges extends to a perfect matching. We shall show that every 5-connected graph of even order embedded on the projective plane and every 6-connected one embedded on the torus and the Klein bottle is 2-extendable and characterize the forbidden structures for 5-connected toroidal graphs to be 2-extendable.
Keywords:
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