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Mickybo Yakari
Mickybo Yakari
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I cannot think of a proof or disproof at the moment but in 'Path factors in cubic graphs', Kawarabayashi, Matsuda and Oda proved that every 2-connected cubic graph of order at least six has a {$P_3$,$P_4$}-factor.  (Actually, they showed that every such graph has a {$P_k$|  $k$≥6}-factor.) I am not sure you can renounce the implicit minimum degree condition and still hope for the same conclusion.

I cannot think of a proof or disproof at the moment but in 'Path factors in cubic graphs', Kawarabayashi, Matsuda and Oda proved that every 2-connected cubic graph of order at least six has a {$P_3$,$P_4$}-factor.(Actually, they showed that every such graph has a {$P_k$|$k$≥6}-factor.) I am not sure you can renounce the implicit minimum degree condition and still hope for the same conclusion.

I cannot think of a proof or disproof at the moment but in 'Path factors in cubic graphs', Kawarabayashi, Matsuda and Oda proved that every 2-connected cubic graph of order at least six has a {$P_3$,$P_4$}-factor.  (Actually, they showed that every such graph has a {$P_k$|  $k$≥6}-factor.) I am not sure you can renounce the implicit minimum degree condition and still hope for the same conclusion.

Source Link
Mickybo Yakari
Mickybo Yakari
  • 364
  • 4
  • 7

I cannot think of a proof or disproof at the moment but in 'Path factors in cubic graphs', Kawarabayashi, Matsuda and Oda proved that every 2-connected cubic graph of order at least six has a {$P_3$,$P_4$}-factor.(Actually, they showed that every such graph has a {$P_k$|$k$≥6}-factor.) I am not sure you can renounce the implicit minimum degree condition and still hope for the same conclusion.