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JGT
2007
14 years 11 months ago
2007
We demonstrate four intrinsically knotted graphs that do not contain each other, nor any previously known intrinsically knotted graph, as a minor.
JGT
2007
14 years 11 months ago
2007
: We present a planar hypohamiltonian graph on 48 vertices, and derive some consequences. © 2007 Wiley Periodicals, Inc. J Graph Theory 55: 338–342, 2007
JGT
2007
14 years 11 months ago
2007
: Let G be a 3-connected planar graph and G∗ be its dual. We show that the pathwidth of G∗ is at most 6 times the pathwidth of G. We prove this result by relating the pathwidth...
JGT
2007
14 years 11 months ago
2007
A graph is uniquely hamiltonian if it contains exactly one hamiltonian cycle. In this note we prove that there are no r-regular uniquely hamiltonian graphs when r > 22. This im...
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JGT
2007
14 years 11 months ago
2007
Let Γ be an infinite, locally finite, connected graph with distance function δ. Given a ray P in Γ and a constant C ≥ 1, a vertex-sequence {xn}∞ n=0 ⊆ V P is said to be...