REVIEW 1 cited by
Planar graphs with the maximum number of induced 6-cycles
Not yet reviewed by Pith; the record is open.
This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.
SPECIMEN: schema-true, not a live event
T0 review · schema-true
One-sentence machine reading of the paper's core claim.
pith:XXXXXXXX · record.json · timestamp
abstract
For large $n$ we determine the maximum number of induced 6-cycles which can be contained in a planar graph on $n$ vertices, and we classify the graphs which achieve this maximum. In particular we show that the maximum is achieved by the graph obtained by blowing up three pairwise non-adjacent vertices in a 6-cycle to sets of as even size as possible, and that every extremal example closely resembles this graph. This extends previous work by the author which solves the problem for 4-cycles and 5-cycles. The 5-cycle problem was also solved independently by Ghosh, Gy\H{o}ri, Janzer, Paulos, Salia, and Zamora.
Forward citations
Cited by 1 Pith paper
-
The maximum number of odd cycles in planar graphs forbidding shorter odd cycles
For every k≥3 and all large n, the maximum number of C_{2k+1} in an n-vertex planar graph with no shorter odd cycle equals the maximum product of k positive integers summing to n-k-1.
Discussion (0). Continue with ORCID to comment.