New extremal edge bounds are proved for K3-free (3n-8), K4-free (floor(7n/2)-7), and K5-free (4n-8) 1-planar graphs, with tightness for large n.
Suzuki,Re-embeddings of maximum 1-planar graphs, SIAM J
2 Pith papers cite this work. Polarity classification is still indexing.
2
Pith papers citing it
citation-role summary
background 1
citation-polarity summary
fields
math.CO 2verdicts
UNVERDICTED 2roles
background 1polarities
background 1representative citing papers
Every 4-connected optimal 2-planar graph is Hamiltonian-connected, with the 4-connectedness condition being sharp via infinitely many 3-connected counterexamples that are non-Hamiltonian.
citing papers explorer
-
Extremal 1-planar graphs without k-cliques
New extremal edge bounds are proved for K3-free (3n-8), K4-free (floor(7n/2)-7), and K5-free (4n-8) 1-planar graphs, with tightness for large n.
-
A note on optimal 2-planar graphs
Every 4-connected optimal 2-planar graph is Hamiltonian-connected, with the 4-connectedness condition being sharp via infinitely many 3-connected counterexamples that are non-Hamiltonian.