A unified FPT framework reduces many crossing-number variants on surfaces to simplicial-complex embeddability, parameterized by genus and crossing bound, with linear or quadratic dependence.
Graphs drawn with few crossings per edge
3 Pith papers cite this work. Polarity classification is still indexing.
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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.
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
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A Unified FPT Framework for Crossing Number Problems
A unified FPT framework reduces many crossing-number variants on surfaces to simplicial-complex embeddability, parameterized by genus and crossing bound, with linear or quadratic dependence.
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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.
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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.