k-restricted edge-connectivity in triangle-free graphs

Authors:
Andreas Holtkamp;Dirk Meierling;Luis Pedro Montejano
Affiliations:
Lehrstuhl C für Mathematik, RWTH Aachen University, 52056 Aachen, Germany;Lehrstuhl II für Mathematik, RWTH Aachen University, 52056 Aachen, Germany;Departament de Matemática Aplicada III, Universitat Politécnica de Catalunya, E08034-Barcelona, Spain
Venue:
Discrete Applied Mathematics
Year:
2012

Citing 3
Cited 1

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Edge-cuts leaving components of order at least three

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Sufficient conditions for triangle-free graphs to be optimally restricted edge-connected

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Abstract

Let G be a @l"k-connected graph. G is called @l"k-optimal, if its k-restricted edge-connectivity @l"k(G) equals its minimum k-edge degree. G is called super-@l"k if every @l"k-cut isolates a connected subgraph of order k. Firstly, we give a lower bound on the order of 2-fragments in triangle-free graphs that are not@l"2-optimal. Secondly, we present an Ore-type condition for triangle-free graphs to be @l"3-optimal. Thirdly, we prove a lower bound on the order of k-fragments in triangle-free @l"k-connected graphs, and use it to show that triangle-free graphs with high minimum degree are @l"k-optimal and super-@l"k.