Displaying similar documents to “A note on minimally 3-connected graphs”

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.

Connectivity of path graphs

Martin Knor, L'udovít Niepel (2000)

Discussiones Mathematicae Graph Theory

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We prove a necessary and sufficient condition under which a connected graph has a connected P₃-path graph. Moreover, an analogous condition for connectivity of the Pₖ-path graph of a connected graph which does not contain a cycle of length smaller than k+1 is derived.