Connected graphs containing a given connected graph as a unique greatest common subgraph.

Gary Chartrand; Mark Johnson

Displaying similar documents to “Connected graphs containing a given connected graph as a unique greatest common subgraph.”

On the structure of $k$ -connected graphs.

Karpov, D.V., Pastor, A.V. (2000)

Zapiski Nauchnykh Seminarov POMI

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Reconstructing the n-Connected Components of a Graph

D.L. GREENWELL, R.L. HEMMINGER (1973)

Aequationes mathematicae

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Graphs without induced P₅ and C₅

Gabor Bacsó, Zsolt Tuza (2004)

Discussiones Mathematicae Graph Theory

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Zverovich [Discuss. Math. Graph Theory 23 (2003), 159-162.] has proved that the domination number and connected domination number are equal on all connected graphs without induced P₅ and C₅. Here we show (with an independent proof) that the following stronger result is also valid: Every P₅-free and C₅-free connected graph contains a minimum-size dominating set that induces a complete subgraph.

Structural Properties of Recursively Partitionable Graphs with Connectivity 2

Olivier Baudon, Julien Bensmail, Florent Foucaud, Monika Pilśniak (2017)

Discussiones Mathematicae Graph Theory

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A connected graph G is said to be arbitrarily partitionable (AP for short) if for every partition (n1, . . . , np) of |V (G)| there exists a partition (V1, . . . , Vp) of V (G) such that each Vi induces a connected subgraph of G on ni vertices. Some stronger versions of this property were introduced, namely the ones of being online arbitrarily partitionable and recursively arbitrarily partitionable (OL-AP and R-AP for short, respectively), in which the subgraphs induced by a partition...