The Set of Circular Flow Numbers of Regular Graphs |
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| Authors: | Michael Schubert Eckhard Steffen |
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| Institution: | 1. PADERBORN INSTITUTE FOR ADVANCED STUDIES IN COMPUTER SCIENCE AND ENGINEERING, PADERBORN UNIVERSITY, PADERBORN, GERMANYFellow of the Graduate School of Dynamic Intelligent Systems.;2. PADERBORN INSTITUTE FOR ADVANCED STUDIES IN COMPUTER SCIENCE AND ENGINEERING, PADERBORN UNIVERSITY, PADERBORN, GERMANY |
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| Abstract: | This article determines the set of the circular flow numbers of regular graphs. Let  be the set of the circular flow numbers of graphs, and  be the set of the circular flow numbers of d‐regular graphs. If d is even, then  . For   it is known 6 that  . We show that  . Hence, the interval  is the only gap for circular flow numbers of  ‐regular graphs between  and 5. Furthermore, if Tutte's 5‐flow conjecture is false, then it follows, that gaps for circular flow numbers of graphs in the interval 5, 6] are due for all graphs not just for regular graphs. |
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| Keywords: | circular flow number nowhere‐zero flows regular graphs |
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