SOME RESULTS ON INTRINSICALLY KNOTTED GRAPHS

DOI10.1142/S021821650700552XzbMath1162.57003MaRDI QIDQ5386832

Joel Foisy, Jacob Hendricks, Paul Blain, Jason LaCombe, Garry S. Bowlin, Thomas R. Fleming

Publication date: 14 May 2008

Published in: Journal of Knot Theory and Its Ramifications (Search for Journal in Brave)

zbMATH Keywords

spatial graphIntrinsically knottedIntrinsically linked

Mathematics Subject Classification ID

Related Items (20)

INTRINSICALLY LINKED GRAPHS WITH KNOTTED COMPONENTS ⋮ Ideal spatial graph configurations ⋮ Intrinsically \(n\)-linked complete graphs ⋮ Bipartite intrinsically knotted graphs with 23 edges ⋮ A new intrinsically knotted graph with 22 edges ⋮ Hadwiger numbers of self-complementary graphs ⋮ TRIANGLE-Y EXCHANGES ON INTRINSIC KNOTTING OF ALMOST COMPLETE AND COMPLETE PARTITE GRAPHS ⋮ Maximal knotless graphs ⋮ Constructions stemming from nonseparating planar graphs and their Colin de Verdière invariant ⋮ Graphs of 20 edges are 2-apex, hence unknotted ⋮ Counting links and knots in complete graphs ⋮ Many, many more intrinsically knotted graphs ⋮ Recent developments in spatial graph theory ⋮ Order nine MMIK graphs ⋮ The 𝐾_{𝑛+5} and 𝐾_{3²,1ⁿ} families and obstructions to 𝑛-apex. ⋮ More intrinsically knotted graphs with 22 edges and the restoring method ⋮ The braid shelf ⋮ INTRINSICALLY KNOTTED GRAPHS HAVE AT LEAST 21 EDGES ⋮ Most graphs are knotted ⋮ Bipartite Intrinsically Knotted Graphs with 22 Edges

Cites Work

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• Graph minors. XX: Wagner's conjecture
• Knots in certain spatial graphs
• Sachs' linkless embedding conjecture
• More intrinsically knotted graphs
• Intrinsically knotted graphs
• A newly recognized intrinsically knotted graph
• INTRINSICALLY n-LINKED GRAPHS
• SOME NEW INTRINSICALLY 3-LINKED GRAPHS
• GRAPHS WITH DISJOINT LINKS IN EVERY SPATIAL EMBEDDING
• Intrinsically triple linked complete graphs

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