# Search results for: Hajo Broersma

Graphs and Combinatorics > 2019 > 35 > 1 > 261-286

Applied Mathematics and Computation > 2018 > 337 > C > 14-24

_{u}denotes the degree of u ∈ V. Bollobás and Erdős (1998) generalized this index by replacing −12 with any fixed real number. To...

Discrete Mathematics > 2017 > 340 > 6 > 1235-1241

Graphs and Combinatorics > 2017 > 33 > 1 > 141-148

*r*such that for every graph

*G*on

*r*vertices, either

*G*contains a $$G_1$$ G 1 or $$\overline{G}$$ G ¯ contains a $$G_2$$ G 2 . A complete bipartite graph $$K_{1,n}$$ K 1 , n is called a star. The...

Discrete Mathematics > 2016 > 339 > 9 > 2284-2287

2016 IEEE Congress on Evolutionary Computation (CEC) > 5238 - 5245

Lecture Notes in Computer Science > Mathematical Foundations of Computer Science 2008 > Contributed Papers > 193-204

*P*

_{ k }-free graphs, i.e., graphs that do not contain a path on

*k*vertices as an induced subgraph. First of all, we show that the pre-coloring extension version of 5-coloring remains NP-complete when restricted to

*P*

_{6}-free graphs. Recent results of Hoàng et al. imply that this problem...

*G*, find a spanning tree

*T*of

*G*such that as many vertices of

*T*as possible have the same degree in

*T*as in

*G*. This problem is a graph-theoretical translation of a problem arising in the system-theoretical context of identifiability in networks, a concept which has applications in e.g., water distribution networks...

Lecture Notes in Computer Science > Structural Information and Communication Complexity > Session 9. Communication Networks: Parallel Computing and Selfish Routing > 328-340

*G*, the minimum number of required rounds is $O{({\sqrt{\alpha}})}$ , where

*α*is the independence number...

*O*(

*n*

^{ 2 }· (¯m+1)) time algorithm to compute the maximum cardinality of an independent set for AT-free graphs, where

*n*is the number...

Lecture Notes in Computer Science > Graph-Theoretic Concepts in Computer Science > Regular Papers > 131-142

*G*=(

*V*,

*E*) and a spanning subgraph

*H*(the backbone) of

*G*, a backbone coloring for

*G*and

*H*is a proper vertex coloring

*V*→{ 1,2,... } in which the colors assigned to adjacent vertices in

*H*differ by at least two. We concentrate on the cases where the backbone is either a spanning tree or a spanning path. For tree...

Lecture Notes in Computer Science > Mathematical Foundations of Computer Science 2004 > Graph Algorithms > 204-214

Lecture Notes in Computer Science > Graph Theoretic Concepts in Computer Science > Regular Talks > 63-74

*P*

_{ k }-free if it does not contain an induced subgraph isomorphic to a path on

*k*vertices. We show that deciding whether a

*P*

_{8}-free graph can be colored with at most four colors is an NP-complete problem. This improves a result of Le, Randerath, and Schiermeyer, who showed that 4-coloring is NP-complete for

*P*

_{9}-free graphs, and a result...

*G*= (

*V*,

*E*) with a capacity function $w : E \longrightarrow \mathbb{Z}^+$ on the edges, the sparsest cut problem is to find a vertex subset

*S*⊂

*V*minimizing ∑

_{ e ∈ E(S,V ∖ S)}

*w*(

*e*)/(|

*S*||

*V*∖

*S*|). This problem is NP-hard. The proof can be found in [16]. In the case of unit capacities (i. e. if

*w*(

*e*) = 1 for every

*e*∈

*E*) the problem is to minimize |

*E*(...

*A*of the vertices of a graph

*G*is an

*asteroidal set*if for each vertex

*a*∈

*A*, the set

*A*∖{

*a*} is contained in one component of

*G-N*[

*a*]. An asteroidal set of cardinality three is called

*asteroidal triple*and graphs without an asteroidal triple are called

*AT-free*. The maximum cardinality of an asteroidal set of

*G*, denoted by an(

*G*), is said to be the

*asteroidal number*of

*G*. We present a scheme...