Displaying similar documents to “Path and cycle factors of cubic bipartite graphs”

Connectivity of path graphs

Martin Knor, L'udovít Niepel (2000)

Discussiones Mathematicae Graph Theory

Similarity:

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.

On Longest Cycles in Essentially 4-Connected Planar Graphs

Igor Fabrici, Jochen Harant, Stanislav Jendroľ (2016)

Discussiones Mathematicae Graph Theory

Similarity:

A planar 3-connected graph G is essentially 4-connected if, for any 3-separator S of G, one component of the graph obtained from G by removing S is a single vertex. Jackson and Wormald proved that an essentially 4-connected planar graph on n vertices contains a cycle C such that [...] . For a cubic essentially 4-connected planar graph G, Grünbaum with Malkevitch, and Zhang showed that G has a cycle on at least ¾ n vertices. In the present paper the result of Jackson and Wormald is improved....