Cycle-saturated graphs of minimum size
نویسندگان
چکیده
منابع مشابه
Constructive Upper Bounds for Cycle-Saturated Graphs of Minimum Size
A graph G is said to be Cl-saturated if G contains no cycle of length l, but for any edge in the complement of G the graph G + e does contain a cycle of length l. The minimum number of edges of a Cl-saturated graph was shown by Barefoot et al. to be between n + c1 n l and n + c2 n l for some positive constants c1 and c2. This confirmed a conjecture of Bollobás. Here we improve the value of c2 f...
متن کاملtKp-saturated graphs of minimum size
A graph G is H-saturated if G does not contain H as a subgraph but for any nonadjacent vertices u and v, G+uv containsH as a subgraph. The parameter sat(H, n) is theminimum number of edges in an H-saturated graph of order n. In this paper, we determine sat(H, n) for sufficiently large nwhen H is a union of cliques of the same order, an arbitrary union of two cliques and a generalized friendship...
متن کاملPm-saturated bipartite graphs with minimum size
A graph G is said to be H-saturated if G is H-free i.e., (G has no subgraph isomorphic to H) and adding any new edge to G creates a copy of H in G. In 1986 L. Kászonyi and Zs. Tuza considered the following problem: for given m and n find the minimum size sat(n;Pm) of Pm-saturated graph of order n. They gave the number sat(n;Pm) for n big enough. We deal with similar problem for bipartite graphs.
متن کاملCycle-Saturated Graphs with Minimum Number of Edges
A graph G is called F -saturated if it does not contain any copy of F , but for any edge e in the complement of G the graph G + e contains some F . The minimum size of an n-vertex F -saturated graph is denoted by sat(n, F ). We give almost exact asymptotics for sat(n,Ck) as k is fixed and n → ∞ where Ck is a cycle with length k.
متن کاملUniquely Cycle-Saturated Graphs
Given a graph F , a graph G is uniquely F -saturated if F is not a subgraph of G and adding any edge of the complement to G completes exactly one copy of F . In this paper we study uniquely Ct-saturated graphs. We prove the following: (1) a graph is uniquely C5-saturated if and only if it is a friendship graph. (2) There are no uniquely C6-saturated graphs or uniquely C7-saturated graphs. (3) F...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1996
ISSN: 0012-365X
DOI: 10.1016/0012-365x(95)00173-t