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Two-coloring the edges of a cubic graph such that each monochromatic component is a path of length at most 5. (English) Zbl 0930.05043
Summary: We prove the conjecture made by J. C. Bermond, J. L. Fouquet, M. Habib and B. Péroche [Discrete Math. 52, 123-132 (1984; Zbl 0556.05054)] that every cubic graph has an edge-coloring as described in the title. The number 5 cannot be replaced by 4. \(\copyright\) Academic Press.

MSC:
05C15 Coloring of graphs and hypergraphs
05C38 Paths and cycles
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