Article ID Journal Published Year Pages File Type
8903844 Journal of Combinatorial Theory, Series B 2018 11 Pages PDF
Abstract
It was conjectured by Jaeger that every 4p-edge-connected graph admits a modulo(2p+1)-orientation (and, therefore, admits a nowhere-zero circular(2+1p)-flow). This conjecture was partially proved by Lovász et al. (2013) [7] for 6p-edge-connected graphs. In this paper, infinite families of counterexamples to Jaeger's conjecture are presented. For p≥3, there are 4p-edge-connected graphs not admitting modulo (2p+1)-orientation; for p≥5, there are (4p+1)-edge-connected graphs not admitting modulo (2p+1)-orientation.
Related Topics
Physical Sciences and Engineering Mathematics Discrete Mathematics and Combinatorics
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