Proper minor-closed families are small
نویسندگان
چکیده
We prove that for every proper minor-closed class I of graphs there exists a constant c such that for every integer n the class I includes at most n!c graphs with vertex-set {1, 2, . . . , n}. This answers a question of Welsh.
منابع مشابه
Node-Weighted Network Design in Planar and Minor-Closed Families of Graphs
We consider node-weighted network design in planar and minor-closed families of graphs. In particular we focus on the edge-connectivity survivable network design problem (EC-SNDP). The input consists of a node-weighted undirected graph G = (V,E) and integral connectivity requirements r(uv) for each pair of nodes uv. The goal is to find a minimum node-weighted subgraph H of G such that, for each...
متن کاملDistributed Almost Exact Approximations for Minor-Closed Families
We give efficient deterministic distributed algorithms which given a graph G from a proper minor-closed family C find an approximation of a minimum dominating set in G and a minimum connected dominating set in G. The algorithms are deterministic and run in a polylogarithmic number of rounds. The approximation accomplished differs from an optimal by a multiplicative factor of (1 + o(1)).
متن کاملStack and Queue Layouts via Layered Separators
It is known that every proper minor-closed class of graphs has bounded stack-number (a.k.a. book thickness and page number). While this includes notable graph families such as planar graphs and graphs of bounded genus, many other graph families are not closed under taking minors. For fixed g and k, we show that every n-vertex graph that can be embedded on a surface of genus g with at most k cro...
متن کاملForbidden minors to graphs with small feedback sets
Finite obstruction set characterizations for lower ideals in the minor order are guaranteed to exist by the Graph Minor Theorem. In this paper we characterize several families of graphs with small feedback sets, namely k1-Feedback Vertex Set, k2-Feedback Edge Set and (k1,k2){Feedback Vertex/Edge Set, for small integer parameters k1 and k2. Our constructive methods can compute obstruction sets f...
متن کاملComputing Planar Intertwines
The proof of Wagner's Conjecture by Robertson and Seymour gives a nite description of any family of graphs which is closed under the minor ordering. This description is a nite set of graphs called the obstructions of the family. Since the intersection and the union of two minor closed graph families is again a minor closed graph family, an interesting question is that of computing the obstructi...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- J. Comb. Theory, Ser. B
دوره 96 شماره
صفحات -
تاریخ انتشار 2006