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- W2476908243 abstract "Let G be a cubic graph with a perfect matching. An edge e of G is a forcing edge if it is contained in a unique perfect matching M , and the perfect matching M is called uniquely forced . In this paper, we show that a 3-connected cubic graph with a uniquely forced perfect matching is generated from K 4 via Y → Δ -operations, i.e., replacing a vertex by a triangle, and further a cubic graph with a uniquely forced perfect matching is 2-connected and contains a triangle. Our result generalizes a previous result of Jiang and Zhang (2011). The unique 3-edge-coloring conjecture asserts that a Petersen-minor-free cubic graph with a unique 3-edge-coloring must contain a triangle. Our result verifies that the unique 3-edge-coloring conjecture holds for a subfamily of uniquely 3-edge-colorable cubic graphs, namely cubic graphs with uniquely forced perfect matching." @default.
- W2476908243 created "2016-08-23" @default.
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- W2476908243 date "2016-12-01" @default.
- W2476908243 modified "2023-10-16" @default.
- W2476908243 title "Uniquely forced perfect matching and unique 3-edge-coloring" @default.
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- W2476908243 doi "https://doi.org/10.1016/j.dam.2016.07.002" @default.
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