๐”– Bobbio Scriptorium
โœฆ   LIBER   โœฆ

Generalizations of the k-factor theorem

โœ Scribed by Sukhamay Kundu

Publisher
Elsevier Science
Year
1974
Tongue
English
Weight
614 KB
Volume
9
Category
Article
ISSN
0012-365X

No coin nor oath required. For personal study only.

โœฆ Synopsis

In this paper, we give a more general sufficient condition for a degree sequence (di) to be realizable by a graph (without multiple edges and loops) containing a subgraph of specified degree sequence tki)* When sequences (di) and (dim ki) are both realizable by graphs, it was shown earlier that the condition k 5 ki 5 k + 1 for all i and some k 2 0 is sufficient for the existence of a (dibgraph containing a (ki)-subgraph. We now show that for k > 1 it is enough to assume, for example, that k 5 ki < k + 1 holds for all i except possibly i = ie, ir, where kio > 0 and ki, > k + 1.

๐Ÿ“œ SIMILAR VOLUMES

On Generalizations of Radon's Theorem an
On Generalizations of Radon's Theorem and the Ham Sandwich Theorem
โœ Helge Tverberg; Siniลกa Vreฤ‡ica ๐Ÿ“‚ Article ๐Ÿ“… 1993 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 211 KB

We raise a conjecture which would generalize Radon's theorem and would provide combinatorial proof for the result from [7], which generalizes Rado's theorem on general measure and the Ham sandwich theorem. We prove that the conjecture holds in several particular cases.

On the Generalizations of the Mazurโ€“Ulam
On the Generalizations of the Mazurโ€“Ulam Isometric Theorem
โœ Wang Jian ๐Ÿ“‚ Article ๐Ÿ“… 2001 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 112 KB

This paper contains several generalizations of the Mazur-Ulam isometric theorem in F \* -spaces which are not assumed to be locally bounded. Let X and Y be two real F \* -spaces, and let X be locally pseudoconvex or ฮด-midpoint bounded. Assume that a operator T maps X onto Y in a ฮด-locally 1/2 i -iso