An excluded minor theorem for the Octahedron plus an edge

2007 ◽  
Vol 57 (2) ◽  
pp. 124-130 ◽  
Author(s):  
John Maharry
Keyword(s):  
Excluded Minor

Random Graphs from a Minor-Closed Class

2009 ◽  
Vol 18 (4) ◽  
pp. 583-599 ◽  
Author(s):  
COLIN McDIARMID
Keyword(s):  
Poisson Distribution ◽  
Random Graph ◽  
Generating Function ◽  
Random Graphs ◽  
Giant Component ◽  
Closed Class ◽  
Exponential Generating Function ◽  
Excluded Minor ◽  
A Minor ◽  
Labelled Graphs

A minor-closed class of graphs is addable if each excluded minor is 2-connected. We see that such a classof labelled graphs has smooth growth; and, for the random graphRnsampled uniformly from then-vertex graphs in, the fragment not in the giant component asymptotically has a simple ‘Boltzmann Poisson distribution’. In particular, asn→ ∞ the probability thatRnis connected tends to 1/A(ρ), whereA(x) is the exponential generating function forand ρ is its radius of convergence.

A Characterization of Almost-Planar Graphs

1996 ◽  
Vol 5 (3) ◽  
pp. 227-245 ◽  
Author(s):  
Bradley S. Gubser
Keyword(s):  
Graph Theory ◽  
Planar Graph ◽  
Planar Graphs ◽  
Explicit Description ◽  
Famous Result ◽  
Minor Criterion ◽  
Excluded Minor

Kuratowski's Theorem, perhaps the most famous result in graph theory, states that K5 and K3,3 are the only non-planar graphs for which both G\e, the deletion of the edge e, and G/e, the contraction of the edge e, are planar for all edges e of G. We characterize the almost-planar graphs, those non-planar graphs for which G\e or G/e is planar for all edges e of G. This paper gives two characterizations of the almost-planar graphs: an explicit description of the structure of almost-planar graphs; and an excluded minor criterion. We also give a best possible bound on the number of edges of an almost-planar graph.

scholarly journals The Structure of Delta-Matroids with Width One Twists

10.37236/7046 ◽  
2018 ◽  
Vol 25 (1) ◽  
Author(s):  
Carolyn Chun ◽  
Rhiannon Hall ◽  
Criel Merino ◽  
Iain Moffatt ◽  
Steven D Noble
Keyword(s):  
Structure Theorem ◽  
Feasible Set ◽  
Excluded Minor ◽  
The Difference

The width of a delta-matroid is the difference in size between a maximal and minimal feasible set. We give a Rough Structure Theorem for delta-matroids that admit a twist of width one. We apply this theorem to give an excluded minor characterisation of delta-matroids that admit a twist of width at most one.

scholarly journals The excluded minor structure theorem with planarly embedded wall

2012 ◽  
Vol 6 (2) ◽  
pp. 187-196
Author(s):  
Bojan Mohar
Keyword(s):  
Structure Theorem ◽  
Excluded Minor

scholarly journals The Minor Crossing Number of Graphs with an Excluded Minor

10.37236/728 ◽  
2008 ◽  
Vol 15 (1) ◽  
Author(s):  
Drago Bokal ◽  
Gašper Fijavž ◽  
David R. Wood
Keyword(s):  
Crossing Number ◽  
Excluded Minor ◽  
A Minor

The minor crossing number of a graph $G$ is the minimum crossing number of a graph that contains $G$ as a minor. It is proved that for every graph $H$ there is a constant $c$, such that every graph $G$ with no $H$-minor has minor crossing number at most $c|V(G)|$.

An Excluded Minor Characterization of Seymour Graphs

2011 ◽  
pp. 1-13 ◽  
Author(s):  
Alexander Ageev ◽  
Yohann Benchetrit ◽  
András Sebő ◽  
Zoltán Szigeti
Keyword(s):  
Excluded Minor

Excluded-Minor Theorems

2011 ◽  
pp. 372-403
Author(s):  
James Oxley
Keyword(s):  
Excluded Minor

scholarly journals On an excluded-minor class of matroids

1990 ◽  
Vol 82 (1) ◽  
pp. 35-52 ◽  
Author(s):  
James G. Oxley
Keyword(s):  
Excluded Minor
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