Cycle spectra of contraction-critically 4-connected planar graphs
Motivated by the long-standing and wide open pancyclicity conjectures of Bondy and Malkevitch, we study the cycle spectra of contraction-critically 4-connected planar graphs. We show that every contraction-critically 4-connected planar graph on n vertices contains a cycle of length k for every k∈⌊n2⌋-⌈n108⌉,⋯,⌊n2⌋+⌊n36⌋∪23n,⋯,n.
Contraction-critically 4-connected graphs
More Funding Information
On-Hei Solomon Lo’s research was partially supported by NSFC Grants 11971406 and 11622110. Jens M. Schmidt’s research was partially supported by the Grant SCHM 3186/2-1 (401348462) from the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation).