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.
Large induced subgraphs with equated maximum degree
β Scribed by Y. Caro; R. Yuster
- Book ID
- 108114187
- Publisher
- Elsevier Science
- Year
- 2010
- Tongue
- English
- Weight
- 440 KB
- Volume
- 310
- Category
- Article
- ISSN
- 0012-365X
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
## Abstract Let __t__(__n, k__) denote the TurΓ‘n numberβthe maximum number of edges in a graph on __n__ vertices that does not contain a complete graph __K__~k+1~. It is shown that if __G__ is a graph on __n__ vertices with __n__ β₯ __k__^2^(__k__ β 1)/4 and __m__ < __t__(__n, k__) edges, then __G__
Let %(n, rn) denote the class of simple graphs on n vertices and rn edges and let G E %(n, rn). There are many results in graph theory giving conditions under which G contains certain types of subgraphs, such as cycles of given lengths, complete graphs, etc. For example, Turan's theorem gives a suff