ROCH THEOREM FOR EDGE - WEIGHTED GRAPHS 3 In [ 2 ] and [ 3 ]
نویسنده
چکیده
We prove a Riemann-Roch theorem for real divisors on edge-weighted graphs over the reals, extending the result of Baker and Norine for integral divisors on graphs with multiple edges.
منابع مشابه
A Riemann-roch Theorem for Edge-weighted Graphs
We prove a Riemann-Roch theorem for real divisors on edgeweighted graphs over the reals, extending the result of Baker and Norine for integral divisors on graphs with multiple edges.
متن کاملRiemann-roch Theory on Finite Sets
In [1] M. Baker and S. Norine developed a theory of divisors and linear systems on graphs, and proved a Riemann-Roch Theorem for these objects (conceived as integer-valued functions on the vertices). In [2] and [3] the authors generalized these concepts to real-valued functions, and proved a corresponding Riemann-Roch Theorem in that setting, showing that it implied the Baker-Norine result. In ...
متن کاملJ an 2 00 7 GRAPHS , ARITHMETIC SURFACES , AND THE RIEMANN - ROCH THEOREM
We use the theory of arithmetic surfaces to show that the Riemann-Roch theorem for Q-graphs is a direct consequence of the usual Riemann-Roch theorem for curves in algebraic geometry.
متن کاملLinear Systems on Edge-weighted Graphs
Let R be any subring of the reals. We present a generalization of linear systems on graphs where divisors are R-valued functions on the set of vertices and graph edges are permitted to have nonnegative weights in R. Using this generalization, we provide an independent proof of a Riemann-Roch formula, which implies the Riemann-Roch formula of Baker and Norine.
متن کاملNode-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 کامل