Extremal Graph for Intersecting Odd Cycles
نویسندگان
چکیده
An extremal graph for a graph H on n vertices is a graph on n vertices with maximum number of edges that does not contain H as a subgraph. Let Tn,r be the Turán graph, which is the complete r-partite graph on n vertices with part sizes that differ by at most one. The well-known Turán Theorem states that Tn,r is the only extremal graph for complete graph Kr+1. Erdős et al. (1995) determined the extremal graphs for intersecting triangles and Chen et al. (2003) determined the maximum number of edges of the extremal graphs for intersecting cliques. In this paper, we determine the extremal graphs for intersecting odd cycles.
منابع مشابه
Random walks and multiply intersecting families
Let F ⊂ 2 be a 3-wise 2-intersecting Sperner family. It is proved that |F| ≤ { ( n−2 (n−2)/2 ) if n even, ( n−2 (n−1)/2 ) + 2 if n odd holds for n ≥ n0. The unique extremal configuration is determined as well.
متن کاملGraphs with large maximum degree containing no odd cycles of a given length
Let us write f(n, ∆; C2k+1) for the maximal number of edges in a graph of order n and maximum degree ∆ that contains no cycles of length 2k + 1. For n 2 ≤ ∆ ≤ n − k − 1 and n sufficiently large we show that f(n, ∆; C2k+1) = ∆(n −∆), with the unique extremal graph a complete
متن کاملOn a conjecture of Erdős and Simonovits: Even cycles
Let F be a family of graphs. A graph is F-free if it contains no copy of a graph in F as a subgraph. A cornerstone of extremal graph theory is the study of the Turán number ex(n,F), the maximum number of edges in an F-free graph on n vertices. Define the Zarankiewicz number z(n,F) to be the maximum number of edges in an F-free bipartite graph on n vertices. Let Ck denote a cycle of length k, an...
متن کاملA spectral condition for odd cycles in graphs
Let G be a graph of su¢ ciently large order n; and let the largest eigenvalue (G) of its adjacency matrix satis es (G) > p bn2=4c: Then G contains a cycle of length t for every t n=320: This condition is sharp: the complete bipartite graph T2 (n) with parts of size bn=2c and dn=2e contains no odd cycles and its largest eigenvalue is equal to p bn2=4c: This condition is stable: if (G) is close t...
متن کامل0n removable cycles in graphs and digraphs
In this paper we define the removable cycle that, if $Im$ is a class of graphs, $Gin Im$, the cycle $C$ in $G$ is called removable if $G-E(C)in Im$. The removable cycles in Eulerian graphs have been studied. We characterize Eulerian graphs which contain two edge-disjoint removable cycles, and the necessary and sufficient conditions for Eulerian graph to have removable cycles h...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Electr. J. Comb.
دوره 23 شماره
صفحات -
تاریخ انتشار 2016