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arXiv · 1707.06745

Nowhere-zero $3$-flow of graphs with small independence number

Jiaao Li·Rong Luo·Yi Wang
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Abstract

Tutte's $3$-flow conjecture states that every $4$-edge-connected graph admits a nowhere-zero $3$-flow. In this paper, we characterize all graphs with independence number at most $4$ that admit a nowhere-zero $3$-flow. The characterization of $3$-flow verifies Tutte's $3$-flow conjecture for graphs with independence number at most $4$ and with order at least $21$. In addition, we prove that every odd-$5$-edge-connected graph with independence number at most $3$ admits a nowhere-zero $3$-flow. To obtain these results, we introduce a new reduction method to handle odd wheels.

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Jiaao Li, Rong Luo, Yi Wang. 2017-07-21. Nowhere-zero $3$-flow of graphs with small independence number. https://arxiv.org/abs/1707.06745

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