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Large induced degenerate subgraphs

✍ Scribed by N. Alon; J. Kahn; P. D. Seymour


Publisher
Springer Japan
Year
1987
Tongue
English
Weight
558 KB
Volume
3
Category
Article
ISSN
0911-0119

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πŸ“œ SIMILAR VOLUMES


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## Abstract Let __G__ be a graph with maximum degree __d__β‰₯ 3 and Ο‰(__G__)≀ __d__, where Ο‰(__G__) is the __clique number__ of the graph __G__. Let __p__~1~ and __p__~2~ be two positive integers such that __d__ = __p__~1~ + __p__~2~. In this work, we prove that __G__ has a vertex partition __S__~1~,

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A colored graph is a graph whose vertices have been properly, though not necessarily optimally colored, with integers. Colored graphs have a natural orientation in which edges are directed from the end point with smaller color to the end point with larger color. A subgraph of a colored graph is colo

Sizes of graphs with induced subgraphs o
✍ Paul ErdΕ‘s; Talmage James Reid; Richard Schelp; William Staton πŸ“‚ Article πŸ“… 1996 πŸ› Elsevier Science 🌐 English βš– 249 KB

Graphs with n + k vertices in which every set of n +j vertices induce a subgraph of maximum degree at least n are considered. For j = 1 and for k fairly small compared to n, we determine the minimum number of edges in such graphs.

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✍ Vladimir Nikiforov πŸ“‚ Article πŸ“… 2009 πŸ› John Wiley and Sons 🌐 English βš– 84 KB

## Abstract In this note we strengthen the stability theorem of ErdΕ‘s and Simonovits. Write __K__~__r__~(__s__~1~, …, __s__~__r__~) for the complete __r__‐partite graph with classes of sizes __s__~1~, …, __s__~__r__~ and __T__~__r__~(__n__) for the __r__‐partite TurΓ‘n graph of order __n__. Our main

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✍ Domingos M. Cardoso; Marcin KamiΕ„ski; Vadim Lozin πŸ“‚ Article πŸ“… 2007 πŸ› Springer US 🌐 English βš– 291 KB
Every tree contains a large induced subg
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Caro et al. proved that every tree of order n contains an induced subgraph of order at least rn/2] with all degrees odd, and conjectured a better bound. In this note we prove that every tree of order n contains an induced subgraph of order at least 2L(n + 1)/3 .] with all degrees odd; this bound is