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On Longest Cycles in Essentially 4-Connected Planar Graphs

100%

Fabrici I., Harant J., Jendroľ S.

Discussiones Mathematicae Graph Theory

2016

tom 36

nr 3

565-575

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. Moreover, new lower bounds on the length of a longest cycle of G are presented if G is an essentially 4-connected planar graph of maximum degree 4 or G is an essentially 4-connected maximal planar graph.

Large Degree Vertices in Longest Cycles of Graphs, I

70%

Li B., Xiong L., Yin J.

Discussiones Mathematicae Graph Theory

2016

tom 36

nr 2

363-382

In this paper, we consider the least integer d such that every longest cycle of a k-connected graph of order n (and of independent number α) contains all vertices of degree at least d.

Ograniczanie wyników

2 Discussiones Mathematicae Graph Theory

1 Fabrici I.

1 Harant J.

1 Jendroľ S.

1 Li B.

1 Xiong L.

1 Yin J.

2 2016

Wyniki wyszukiwania

On Longest Cycles in Essentially 4-Connected Planar Graphs

Large Degree Vertices in Longest Cycles of Graphs, I