On scaling to an integer matrix and graphs with integer weighted cycles
نویسندگان
چکیده
منابع مشابه
Bipartite subgraphs of integer weighted graphs
For every integer p > 0 let f(p) be the minimum possible value of the maximum weight of a cut in an integer weighted graph with total weight p. It is shown that for every large n and every m < n, f( ( n 2 ) + m) = b 2 4 c + min(d n 2 e, f(m)). This supplies the precise value of f(p) for many values of p including, e.g, all p = ( n 2 ) + ( m 2 ) when n is large enough and m 2 4 ≤ n 2 .
متن کاملTurán problems for integer-weighted graphs
A multigraph is (k, r)-dense if every k-set spans at most r edges. What is the maximum number of edges exN(n, k, r) in a (k, r)-dense multigraph on n vertices? We determine the maximum possible weight of such graphs for almost all k and r (e.g., for all r > k) by determining a constant m = m(k, r) and showing that exN(n, k, r) = m ( n 2 ) +O(n), thus giving a generalization of Turán’s theorem. ...
متن کاملINTEGER-MAGIC SPECTRA OF CYCLE RELATED GRAPHS
For any h in N , a graph G = (V, E) is said to be h-magic if there exists a labeling l: E(G) to Z_{h}-{0} such that the induced vertex set labeling l^{+: V(G) to Z_{h}} defined by l^{+}(v)= Summation of l(uv)such that e=uvin in E(G) is a constant map. For a given graph G, the set of all for which G is h-magic is called the integer-magic spectrum of G and is denoted by IM(G). In this paper, the ...
متن کاملInteger program with bimodular matrix
Let A be an m × n integral matrix of rank n. We say that A is bimodular if the maximum of the absolute values of the n×n minors is at most 2. We give a polynomial time algorithm that finds an integer solution for system Ax ≤ b. A polynomial time algorithm for integer program max{cx : Ax ≤ b} is constructed proceeding on some assumptions.
متن کاملAn Integer Programming Model and a Tabu Search Algorithm to Generate α-labeling of Special Classes of Quadratic Graphs
First, an integer programming model is proposed to find an α-labeling for quadratic graphs. Then, a Tabu search algorithm is developed to solve large scale problems. The proposed approach can generate α-labeling for special classes of quadratic graphs, not previously reported in the literature. Then, the main theorem of the paper is presented. We show how a problem in graph theory c...
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: Linear Algebra and its Applications
سال: 2016
ISSN: 0024-3795
DOI: 10.1016/j.laa.2016.01.018