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

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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.

On Longest Cycles in Essentially 4-Connected Planar Graphs

Igor Fabrici, Jochen Harant, Stanislav Jendroľ (2016)

Discussiones Mathematicae Graph Theory

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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....

The i-chords of cycles and paths

Terry A. McKee (2012)

Discussiones Mathematicae Graph Theory

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An i-chord of a cycle or path is an edge whose endpoints are a distance i ≥ 2 apart along the cycle or path. Motivated by many standard graph classes being describable by the existence of chords, we investigate what happens when i-chords are required for specific values of i. Results include the following: A graph is strongly chordal if and only if, for i ∈ {4,6}, every cycle C with |V(C)| ≥ i has an (i/2)-chord. A graph is a threshold graph if and only if, for i ∈ {4,5}, every path...