# Search results for: Bruce Reed

Random Structures & Algorithms > 55 > 2 > 290 - 312

*G*obtained by starting with a single vertex of

*G*and repeatedly selecting, uniformly at random, an edge of

*G*with exactly one endpoint in

*T*and adding this edge to

*T*.

Mathematical Programming > 2018 > 171 > 1-2 > 519-522

Probability Theory and Related Fields > 2018 > 170 > 1-2 > 263-310

*i*has degree $$d_i$$ d i . In this paper we determine whether $$G({\mathcal {D}})$$ G ( D ) has a giant component with high...

NeuroImage: Clinical > 2017 > 13 > C > 130-137

Bolyai Society Mathematical Studies > An Irregular Mind > 405-414

*skew partition*of a graph

*G*to be a partition of its vertex set into two non-empty parts

*A*and

*B*such that

*A*induces a disconnected subgraph of

*G*and

*B*induces a disconnected subgraph of . Skew partitions are important in the characterization of perfect graphs. De Figuereido et al. presented a polynomial time algorithm which given a graph either finds a skew partition...

Lecture Notes in Computer Science > Integer Programming and Combinatorial Optimization > Algorithms > 137-152

*G*and a collection of pairs of distinct vertices (

*s*

_{i};

*t*

_{i}) of

*G*, find a small- est set of edges of

*G*whose removal disconnects each

*s*

_{i}from the corre- sponding

*t*

_{i}. Our main result is a polynomial-time approximation scheme for Multicut in unweighted graphs with bounded degree and bounded tree-width:...

*K*

_{5}as a minor and outputs a

*K*

_{5}-model if the input graph contains one. If the input graph has no

*K*

_{5}-minor then the algorithm constructs a tree decomposition such that each node of the tree corresponds to a planar graph or a graph with eight vertices. Such a decomposition can be used...

*star coloring*of an undirected graph

*G*is a proper vertex coloring of

*G*(i.e., no two neighbors are assigned the same color) such that any path of length 3 in

*G*is not bicolored. We give the exact value of the star chromatic number of different families of graphs such as trees, cycles, complete bipartite graphs, outerplanar...

*δ*. Our results are obtained via the probabilistic method.

*n*and girth

*g*have domination number at most 0.32127 $n+O\left(\frac{n}{g}\right)$ .

*k*, determines whether an input graph

*G*= (

*V,E*) has treewidth

*k*and, if so, constructs a tree decomposition of

*G*of width at most

*k*. Our algorithm has the following additional feature: if G has treewidth greater than

*k*then a subgraph

*G*′ of

*G*of treewidth greater than

*k*is returned along with a tree decomposition of...

Lecture Notes in Computer Science > LATIN 2000: Theoretical Informatics > Web Graph, Graph Theory I > 126-134

*G*of bounded , given the bounded width decomposition of

*G*, every optimization, enumeration or evaluation problem that can be defined by a Monadic Second Order Logic formula using quantifiers on vertices but...

Neurobiology of Aging > 2016 > 40 > C > 173-180

Alzheimer's & Dementia: The Journal of the Alzheimer's Association > 2015 > 11 > 7 Supplement > P447-P448