• Corpus ID: 221970544

Unavoidable Induced Subgraphs of Large 2-Connected Graphs

@article{Allred2020UnavoidableIS,
  title={Unavoidable Induced Subgraphs of Large 2-Connected Graphs},
  author={Sarah Allred and Guoli Ding and Bogdan Oporowski},
  journal={arXiv: Combinatorics},
  year={2020}
}
Ramsey proved that for every positive integer $n$, every sufficiently large graph contains an induced $K_n$ or $\overline{K}_n$. Among the many extensions of Ramsey's Theorem there is an analogue for connected graphs: for every positive integer $n$, every sufficiently large connected graph contains an induced $K_n$, $K_{1,n}$, or $P_n$. In this paper, we establish an analogue for 2-connected graphs. In particular, we prove that for every integer exceeding two, every sufficiently large 2… 

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References

SHOWING 1-10 OF 12 REFERENCES
On a Problem of Formal Logic
This paper is primarily concerned with a special case of one of the leading problems of mathematical logic, the problem of finding a regular procedure to determine the truth or falsity of any given
Amsterdam
HAZENBERG, T. 2000. Leiden-Roomburg 1995-1997, archeologisch onderzoek naar het kanaal van Corbulo en de vicus van het castellum Matilo, Rapportages Archeologische Monumentenzorg, 77, Amersfoort:
Unavoidable Minors of Large 3-Connected Matroids
This paper proves that, for every integernexceeding two, there is a numberN(n) such that every 3-connected matroid with at leastN(n) elements has a minor that is isomorphic to one of the following
Unavoidable Minors of Large 3-Connected Binary Matroids
We show that, for every integerngreater than two, there is a numberNsuch that every 3-connected binary matroid with at leastNelements has a minor that is isomorphic to the cycle matroid ofK3,n, its
Graph theory
Introduction to the Theory of Matroids
I. Equivalent Axiomatic Definitions and Elementary Properties of Matroids.- 1.1. The first rank-axiomatic definition of a matroid.- 1.2. The independence-axiomatic definition of a matroid.- 1.3. The
A Ramsey-type theorem for traceable graphs☆
Unavoidable parallel minors of 4‐connected graphs
TLDR
It is proved that, for any positive integer k, every internally 4-connected graph of sufficiently high order contains a parallel minor isomorphic to a variation of K_{4,k} with a complete graph on the vertices of degree k.
Editors
  • Computer Science
    Brain Research Bulletin
  • 1986
Typical Subgraphs of 3- and 4-Connected Graphs
TLDR
It is proved that, for every positive integer k, there is an integer N such that every 3-connected graph with at least N vertices has a minor isomorphic to the k -spoke wheel or K 3, k ; and that every internally 4-connected graphs has aMinor isomorphism to the 2 k-spoke double wheel, the k-rung circular ladder, thek -rung Mobius ladder, or K 4, k.
...
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