Covering Planar Graphs with a Fixed Number of Balls
نویسندگان
چکیده
In this note, we prove that there exists a constant ρ such that any planar graph G of diameter ≤ 2R can be covered with at most ρ balls of radius R, a result conjectured by C. Gavoille, D. Peleg, A. Raspaud, and E. Sopena in 2001.
منابع مشابه
Covering nearly surface-embedded graphs with a fixed number of balls
A recent result of Chepoi, Estellon and Vaxes [Disc. Comp. Geom. ’07] states that any planar graph of diameter at most 2R can be covered by a constant number of balls of size R; put another way, there are a constant-sized subset of vertices within which every other vertex is distance half the diameter. We generalize this result to graphs embedded on surfaces of fixed genus with a fixed number o...
متن کاملThree ways to cover a graph
We consider the problem of covering a host graph G with several graphs from a fixed template class T . The classical covering number of G with respect to T is the minimum number of template graphs needed to cover the edges of G. We introduce two new parameters: the local and the folded covering number. Each parameter measures how far G is from the template class in a different way. Whereas the ...
متن کاملPacking and covering δ-hyperbolic spaces by balls
We consider the problem of covering and packing subsets of δ-hyperbolic metric spaces and graphs by balls. These spaces, defined via a combinatorial Gromov condition, have recently become of interest in several domains of computer science. Specifically, given a subset S of a δhyperbolic graph G and a positive number R, let γ(S, R) be the minimum number of balls of radius R covering S. It is kno...
متن کاملDetour Monophonic Graphoidal Covering Number of Corona Product Graph of Some Standard Graphs with the Wheel
A chord of a path $P$ is an edge joining two non-adjacent vertices of $P$. A path $P$ is called a monophonic path if it is a chordless path. A longest $x-y$ monophonic path is called an $x-y$ detour monophonic path. A detour monophonic graphoidal cover of a graph $G$ is a collection $psi_{dm}$ of detour monophonic paths in $G$ such that every vertex of $G$ is an internal vertex of at most on...
متن کاملParameterized Algorithms for Partial Cover Problems
Covering problems are fundamental classical problems in optimization, computer science and complexity theory. Typically an input to these problems is a family of sets over a finite universe and the goal is to cover the elements of the universe with as few sets of the family as possible. The variations of covering problems include well known problems like Set Cover, Vertex Cover, Dominating Set ...
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:
- Discrete & Computational Geometry
دوره 37 شماره
صفحات -
تاریخ انتشار 2007