On removable even circuits in graphs |
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Authors: | P.A. Sinclair |
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Affiliation: | Department of Mathematics, College of Natural Sciences, University of Ulsan, P.O. Box 18, Ulsan 680749, Republic of Korea |
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Abstract: | Let G be a connected graph with minimum degree at least 3. We prove that there exists an even circuit C in G such that G−E(C) is either connected or contains precisely two components one of which is isomorphic to a 1-bond. We further prove sufficient conditions for there to exist an even circuit C in a 2-connected simple graph G such that G−E(C) is 2-connected. As a consequence of this, we obtain sufficient conditions for there to exist an even circuit C in a 2-connected graph G for which G−E(C) is 2-connected. |
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Keywords: | Removable even circuits |
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