Results 31 to 40 of about 310,485 (285)
Faster exponential-time algorithms in graphs of bounded average degree [PDF]
, 2013 We first show that the Traveling Salesman Problem in an n-vertex graph with average degree bounded by d can be solved in O*(2^{(1-\eps_d)n}) time and exponential space for a constant \eps_d depending only on d, where the O*-notation suppresses factors ...
A. Björklund +6 more
core +2 more sources
Limit laws of planar maps with prescribed vertex degrees [PDF]
Combinatorics, Probability and Computing, 2019 AbstractWe prove a generalmulti-dimensional central limit theorem for the expected number of vertices of a given degree in the family of planar maps whose vertex degrees are restricted to an arbitrary (finite or infinite) set of positive integersD. Our results rely on a classical bijection with mobiles (objects exhibiting a tree structure), combined ...
Collet, G., Drmota, M., Klausner, L. D.
openaire +2 more sources
Minimum generalized degree distance of n-vertex tricyclic graphs [PDF]
Journal of Inequalities and Applications, 2013 Abstract In (Hamzeh et al. in Stud. Univ. Babeş-Bolyai, Chem., 4:73-85, 2012), we introduced a generalization of a degree distance of graphs as a new topological index. In this paper, we characterize the n-vertex tricyclic graphs which have the minimum generalized degree distance. MSC:05C12, 05C35, 05C05.
Hamzeh, Asma +2 more
openaire +2 more sources
Vertex degrees of planar graphs
Journal of Combinatorial Theory, Series B, 1979 AbstractLet G be a planar graph having n vertices with vertex degrees d1, d2,…,dn. It is shown that Σi=1ndi2 ≤ 2n2 + O(n). The main term in this upper bound is best possible.
openaire +1 more source
Bounding the feedback vertex number of digraphs in terms of vertex degrees
Discrete Applied Mathematics, 2011 The Turan bound is a famous result in graph theory, which relates the independence number of an undirected graph to its edge density. Also the Caro-Wei inequality, which gives a more refined bound in terms of the vertex degree sequence of a graph, might be regarded today as a classical result. We show how these statements can be generalized to directed
openaire +3 more sources
Random Graphs' Robustness in Random Environment
Austrian Journal of Statistics, 2017 We consider configuration graphs the vertex degrees of which are independent and follow the power-law distribution. Random graphs dynamics takes place in a random environment with the parameter of vertex degree distribution following uniform ...
Marina Leri, Yury Pavlov
doaj +1 more source
Dynamics of heuristic optimization algorithms on random graphs
, 2002 In this paper, the dynamics of heuristic algorithms for constructing small vertex covers (or independent sets) of finite-connectivity random graphs is analysed. In every algorithmic step, a vertex is chosen with respect to its vertex degree. This vertex,
Weigt, Martin
core +1 more source
The minimum vertex degree for an almost-spanning tight cycle in a $3$-uniform hypergraph [PDF]
, 2016 We prove that any $3$-uniform hypergraph whose minimum vertex degree is at least $\left(\frac{5}{9} + o(1) \right)\binom{n}{2}$ admits an almost-spanning tight cycle, that is, a tight cycle leaving $o(n)$ vertices uncovered.
Cooley, Oliver, Mycroft, Richard
core +2 more sources
Conjecture Involving Arithmetic-Geometric and Geometric-Arithmetic Indices
Discrete Dynamics in Nature and Society, 2022 The geometric-arithmetic (GA) index of a graph G is the sum of the ratios of geometric and arithmetic means of end-vertex degrees of edges of G. Similarly, the arithmetic-geometric (AG) index of G is defined. Recently, Vujošević et al. conjectured that a
Zainab Alsheekhhussain +3 more
doaj +1 more source
Improved Algorithm for Degree Bounded Survivable Network Design Problem
, 2009 We consider the Degree-Bounded Survivable Network Design Problem: the objective is to find a minimum cost subgraph satisfying the given connectivity requirements as well as the degree bounds on the vertices.
K. Chaudhuri +8 more
core +2 more sources