Filters

362,406 Hits in 4.0 sec

### On Unique Independence Weighted Graphs [article]

Farzad Didehvar, Ali D. Mehrabi, Fatemeh Raee B
2009 arXiv   pre-print
A vertex-weighted graph G is called a unique independence vertex-weighted graph if it has a unique independent set with maximum sum of weights.  ...  ; we give, however, some combinatorial characterizations of unique independence vertex-weighted graphs.  ...  Neighborhood-based characterization of unique independence weighted graphs In this section, we try to state some theorems on characterizations of unique weighted graphs mainly based on the neighborhood  ...

### Inapproximability of Vertex Cover and Independent Set in Bounded Degree Graphs

Per Austrin, Subhash Khot, Muli Safra
2009 2009 24th Annual IEEE Conference on Computational Complexity
We study the inapproximability of Vertex Cover and Independent Set on degree d graphs.  ...  . • Independent Set is Unique Games-hard to approximate to within a factor O( d log 2 d ). This improves the Unique Games hardness result of Samorodnitsky and Trevisan  .  ...  Then for all sufficiently small γ > 0, there is an algorithm which, on input a Unique Games instance Λ = (U,V, E, Π, L) outputs a weighted graph G with the following properties: • Completeness: If IndOpt  ...

### Maximum Weight Independent Sets and Matchings in Sparse Random Graphs. Exact Results using the Local Weak Convergence Method [article]

David Gamarnik, Tomasz Nowicki, Grzegorz Swirscsz
2003 arXiv   pre-print
weight of an independent set.  ...  In this paper we assume in addition that the nodes of the graph are equipped with non-negative weights, independently generated according to some common distribution, and we consider instead the maximum  ...  Clearly it is the unique fixed point of T since any fixed point of T is also a fixed point of T 2 . 2 We now switch to analyzing the maximum weight independent set problem on a tree.  ...

### Page 648 of Mathematical Reviews Vol. , Issue 91B [page]

1991 Mathematical Reviews
A tree is also said to be a unique independence tree if it has a largest independent set of vertices J; if moreover the complement of / is also independent then the tree is called a strong unique independence  ...  It is also shown that no bivariegated tree is a unique independence tree and also that if a pseudobivariegated tree is a unique independence tree then it is a strong unique inde- pendence tree. J.  ...

### Maximum weight independent sets and matchings in sparse random graphs. Exact results using the local weak convergence method

David Gamarnik, Tomasz Nowicki, Grzegorz Swirszcz
2005 Random structures & algorithms (Print)
weight of an independent set.  ...  In this paper we assume in addition that the nodes of the graph are equipped with nonnegative weights, independently generated according to some common distribution, and we consider instead the maximum  ...  The authors also wish to thank Antar Bandyopadhyay for correcting an earlier version of the manuscript, and Nick Wormald for informing the authors on the state of the art results on largest independent  ...

### Matching is as easy as matrix inversion

Ketan Mulmuley, Umesh V. Vazirani, Vijay V. Vazirani
1987 Proceedings of the nineteenth annual ACM conference on Theory of computing - STOC '87
A new algorithm for finding a maximum matching in a general graph is presented; its special feature being that the only computationally non-trivial step required in its execution is the inversion of a  ...  The CLIQUE problem is 'Given a graph G(V, E) and an integer k, is there a clique of size k in the graph?' On the other hand, UNIQUE CLIQUE asks if there is exactly one clique of size k.  ...  Notice that the proof of the isolating lemma relies on the independence of the weights of the elements. It would be interesting to study how crucial the role of independence is.  ...

### Matching is as easy as matrix inversion

Ketan Mulmuley, Umesh V. Vazirani, Vijay V. Vazirani
1987 Combinatorica
A new algorithm for finding a maximum matching in a general graph is presented; its special feature being that the only computationally non-trivial step required in its execution is the inversion of a  ...  The CLIQUE problem is 'Given a graph G(V, E) and an integer k, is there a clique of size k in the graph?' On the other hand, UNIQUE CLIQUE asks if there is exactly one clique of size k.  ...  Notice that the proof of the isolating lemma relies on the independence of the weights of the elements. It would be interesting to study how crucial the role of independence is.  ...

### Decomposition by clique separators

Robert E. Tarjan
1985 Discrete Mathematics
We describe how such a decomposition can be used in divide-and-conquer algorithms for various graph problems, such as graph coloring and finding maximum independent sets.  ...  We consider the problem of decomposing a graph by means of clique separators, by which we mean finding cliques (complete graphs) whose removal disconnects the graph.  ...  Acknowledgment My thanks to Marty Golumbic, whose lecture on EPT graphs stimulated this research.  ...

### Distinguishing graphs by their left and right homomorphism profiles

Delia Garijo, Andrew Goodall, Jaroslav Nešetřil
2011 European journal of combinatorics (Print)
We introduce a new property of graphs called 'q-state Potts uniqueness' and relate it to chromatic and Tutte uniqueness, and also to 'chromatic-flow uniqueness', recently studied by Duan, Wu and Yu.  ...  We establish for which edge-weighted graphs H homomorphism functions from multigraphs G to H are specializations of the Tutte polynomial of G, in particular answering a question of Freedman, Lovász and  ...  A bivariate version of the independence polynomial is I(G; x, y) = − independent sets U⊆V x |U| y |V \U| = y |V | I(G; x/y).Twin vertices in an edge-weighted graph H on vertex set [q] with adjacency matrix  ...

### A weighted graph problem from commutative algebra [article]

Peter M. Johnson
2011 arXiv   pre-print
We give an especially simple proof of a theorem in graph theory that forms the key part of the solution to a problem in commutative algebra, on how to characterize the integral closure of a polynomial  ...  Our focus is on the problem as one that merely concerns weighted graphs, but motivating background from commutative algebra will first be sketched.  ...  After the reduction via h, no vertex v of G f can lie on a unique edge. Thus the graph G f is a disjoint union of odd cycles, some perhaps loops.  ...

### A tolerance-based heuristic approach for the weighted independent set problem

B. I. Goldengorin, D. S. Malyshev, P. M. Pardalos, V. A. Zamaraev
2013 Journal of combinatorial optimization
Several computational experiments show that our heuristics works very well on graphs of a small density.  ...  In this paper we suggest a tolerance-based polynomial heuristic algorithm for the weighted independent set problem.  ...  One can easily verify that the found solution {x 1 , x 4 } is also the unique optimal independent set of the initial graph.  ...

### Ties in ranking scores can be treated as weighted samples [article]

Mark Tygert
2022 arXiv   pre-print
Prior proposals for cumulative statistics suggest making tiny random perturbations to the scores (independent variables in a regression) in order to ensure the scores' uniqueness.  ...  This reduces the problem of analyzing data with scores that may not be unique to the problem of analyzing a weighted data set with scores that are unique by construction.  ...  The graphs of the earlier analyses directly displayed all members of the original data set, omitting no one.  ...

### The Maximum Degree of an Exponentially Distributed Random Graph

Desti Alannora Harahap, Saib Suwilo, Mardiningsih Mardiningsih
2022 SinkrOn
Let G G (n, p) be a graph on n vertices where each pair of vertices is joined independently with probability p for 0 < p < 1 and q = 1 p.  ...  In this work, we introduce weighted random graf G with exponential distribution and investigate that the probability that every vertex of G has degree at most np + b√pqn is equal to 0.595656764.  ...  ., 2018) have studied the weighted random graph model for the case of large networks.  ...

### Forthcoming papers

1990 Discrete Mathematics
weighted degrees of the vertices become distinct. shows that every additive set is a set of uniqueness.  ...  Shepp, Sets uniquely determined by projections on axes II. Discrete case.  ...

### Randomized Techniques for Parameterized Algorithms [chapter]

Dániel Marx
2012 Lecture Notes in Computer Science
The probability that there is a unique S ∈ F having minimum weight is at least 1 − |U| N .  ...  By setting N := |V (G )| O(1) , we can assume that there is a unique minimum weight Hamiltonian cycle. If N is polynomial in the input size, we can guess this minimum weight.  ...  If there is a unique weight-C Hamiltonian cycle: the number of weight-C colored cycle covers is 2 mod 4. Assign random weights ≤ 2|E (G )| to the edges.  ...
« Previous Showing results 1 — 15 out of 362,406 results