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Long cycles in graphs with large degree sums

โœ Scribed by Douglas Bauer; H.J. Veldman; A. Morgana; E.F. Schmeichel


Publisher
Elsevier Science
Year
1990
Tongue
English
Weight
764 KB
Volume
79
Category
Article
ISSN
0012-365X

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๐Ÿ“œ SIMILAR VOLUMES


Long cycles in graphs with large degree
โœ Van den Heuvel, J. ๐Ÿ“‚ Article ๐Ÿ“… 1996 ๐Ÿ› John Wiley and Sons ๐ŸŒ English โš– 801 KB

We present and prove several results concerning the length of longest cycles in 2connected or I-tough graphs with large degree sums. These results improve many known results on long cycles in these graphs. We also consider the sharpness of the results and discuss some possible strengthenings.

Relative length of long paths and cycles
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## Abstract For a graph __G, p__(__G__) denotes the order of a longest path in __G__ and __c__(__G__) the order of a longest cycle. We show that if __G__ is a connected graph __n__ โ‰ฅ 3 vertices such that __d__(__u__) + __d__(__v__) + __d__(__w__) โ‰ง n for all triples __u, v, w__ of independent verti

Cycles and paths in graphs with large mi
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## Abstract Let __G__ be a simple graph of order __n__ and minimal degree >โ€‰cn (0โ€‰<โ€‰cโ€‰<โ€‰1/2). We prove that (1) There exist __n__~0~โ€‰=โ€‰__n__~0~(__c__) and __k__โ€‰=โ€‰__k__(__c__) such that if __n__โ€‰>โ€‰__n__~0~ and __G__ contains a cycle __C__~__t__~ for some __t__โ€‰>โ€‰2__k__, then __G__ contains a cycle

Cycle lengths in graphs with large minim
โœ V. Nikiforov; R. H. Schelp ๐Ÿ“‚ Article ๐Ÿ“… 2006 ๐Ÿ› John Wiley and Sons ๐ŸŒ English โš– 114 KB ๐Ÿ‘ 1 views

## Abstract Our main result is the following theorem. Let __k__โ€‰โ‰ฅโ€‰2 be an integer, __G__ be a graph of sufficiently large order __n__, and __ฮด__(__G__)โ€‰โ‰ฅโ€‰__n__/__k__. Then: __G__ contains a cycle of length __t__ for every even integer __t__โ€‰โˆˆโ€‰[4, __ฮด__(__G__)โ€‰+โ€‰1]. If __G__ is nonbipartite then