Extremal graphs without long paths and large cliques
European Journal of Combinatorics(2023)
Abstract
Let F be a family of graphs. A graph is called F-free if it does not contain any member of F as a subgraph. The Turán number of F is the maximum number of edges in an n-vertex F-free graph and is denoted by ex(n,F). The same maximum under the additional condition that the graphs are connected is exconn(n,F). Let Pk be the path on k vertices, Km be the clique on m vertices. We determine ex(n,{Pk,Km}) if k>2m−1 and exconn(n,{Pk,Km}) if k>m for sufficiently large n.
MoreTranslated text
Key words
extremal graphs,long paths
AI Read Science
Must-Reading Tree
Example
![](https://originalfileserver.aminer.cn/sys/aminer/pubs/mrt_preview.jpeg)
Generate MRT to find the research sequence of this paper
Chat Paper
Summary is being generated by the instructions you defined