An improved linear edge bound for graph linkages
نویسندگان
چکیده
منابع مشابه
An improved linear edge bound for graph linkages
A graph is said to be k-linked if it has at least 2k vertices and for every sequence s1, . . . , sk, t1, . . . , tk of distinct vertices there exist disjoint paths P1, . . . , Pk such that the ends of Pi are si and ti. Bollobás and Thomason showed that if a simple graph G on n vertices is 2k-connected and G has at least 11kn edges, then G is k-linked. We give a relatively simple inductive proof...
متن کاملSome Edge Cut Sets and an Upper bound for Edge Tenacity of Organic Compounds CnH2n+2
The graphs play an important role in our daily life. For example, the urban transport network can be represented by a graph, as the intersections are the vertices and the streets are the edges of the graph. Suppose that some edges of the graph are removed, the question arises, how damaged the graph is. There are some criteria for measuring the vulnerability of graph; the...
متن کاملAn upper bound for the regularity of powers of edge ideals
A recent result due to Ha and Van Tuyl proved that the Castelnuovo-Mumford regularity of the quotient ring $R/I(G)$ is at most matching number of $G$, denoted by match$(G)$. In this paper, we provide a generalization of this result for powers of edge ideals. More precisely, we show that for every graph $G$ and every $sgeq 1$, $${rm reg}( R/ I(G)^{s})leq (2s-1) |E(G)|^{s-1} {rm ma...
متن کاملImproved Complexity Bound of Vertex Cover for Low degree Graph
In this paper, we use a new method to decrease the parameterized complexity bound for finding the minimum vertex cover of connected max-degree-3 undirected graphs. The key operation of this method is reduction of the size of a particular subset of edges which we introduce in this paper and is called as “real-cycle” subset. Using “realcycle” reductions alone we compute a complexity bound O(1.158...
متن کاملImproved Monotone Circuit Depth Upper Bound for Directed Graph Reachability
We prove that the directed graph reachability problem (transitive closure) can be solved by monotone fan-in 2 boolean circuits of depth (1/2+o(1))(log n)^2, where n is the number of nodes. This improves the previous known upper bound (1+o(1))(log n)^2. The proof is non-constructive, but we give a constructive proof of the upper bound (7/8+o(1))(log n)^2.
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: European Journal of Combinatorics
سال: 2005
ISSN: 0195-6698
DOI: 10.1016/j.ejc.2004.02.013