Removing two adjacent vertices from a cyclically 4-edge-connected cubic planar graph Y yields a graph H that contains a cycle of length between k and 3k/2 if its circumference is at least even k >= 4, implying that the line graph of Y has cycles of every length l in {3} union {5 to |V|-1} avoiding a
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A note on cycles in cyclically $4$-edge-connected cubic planar graphs
Removing two adjacent vertices from a cyclically 4-edge-connected cubic planar graph Y yields a graph H that contains a cycle of length between k and 3k/2 if its circumference is at least even k >= 4, implying that the line graph of Y has cycles of every length l in {3} union {5 to |V|-1} avoiding a