All Outputs (158)

λ-backbone colorings along pairwise disjoint stars and matchings (2009)
Journal Article
Broersma, H., Fujisawa, J., Marchal, L., Paulusma, D., Salman, A., & Yoshimoto, K. (2009). λ-backbone colorings along pairwise disjoint stars and matchings. Discrete Mathematics, 309(18), 5596-5609. https://doi.org/10.1016/j.disc.2008.04.007

Given an integer λ≥2, a graph G=(V,E) and a spanning subgraph H of G (the backbone of G), a λ-backbone coloring of (G,H) is a proper vertex coloring V→{1,2,…} of G, in which the colors assigned to adjacent vertices in H differ by at least λ. We study... Read More about λ-backbone colorings along pairwise disjoint stars and matchings.

Covering graphs with few complete bipartite subgraphs (2009)
Journal Article
Fleischner, H., Mujuni, E., Paulusma, D., & Szeider, S. (2009). Covering graphs with few complete bipartite subgraphs. Theoretical Computer Science, 410(21-23), 2045-2053. https://doi.org/10.1016/j.tcs.2008.12.059

We consider computational problems on covering graphs with bicliques (complete bipartite subgraphs). Given a graph and an integer k, the biclique cover problem asks whether the edge-set of the graph can be covered with at most k bicliques; the bicliq... Read More about Covering graphs with few complete bipartite subgraphs.

Backbone colorings along stars and matchings in split graphs: their span is close to the chromatic number (2009)
Journal Article
Broersma, H., Marchal, L., Paulusma, D., & Salman, A. (2009). Backbone colorings along stars and matchings in split graphs: their span is close to the chromatic number. Discussiones Mathematicae. Graph Theory, 29(1), 143-162. https://doi.org/10.7151/dmgt.1437

We continue the study on backbone colorings, a variation on classical vertex colorings that was introduced at WG2003. Given a graph G = (V,E) and a spanning subgraph H of G (the backbone of G), a l-backbone coloring for G and H is a proper vertex col... Read More about Backbone colorings along stars and matchings in split graphs: their span is close to the chromatic number.

Upper bounds and algorithms for parallel knock-out numbers (2009)
Journal Article
Broersma, H., Johnson, M., & Paulusma, D. (2009). Upper bounds and algorithms for parallel knock-out numbers. Theoretical Computer Science, 410(14), 1319-1327. https://doi.org/10.1016/j.tcs.2008.03.024

We study parallel knock-out schemes for graphs. These schemes proceed in rounds in each of which each surviving vertex simultaneously eliminates one of its surviving neighbours; a graph is reducible if such a scheme can eliminate every vertex in the... Read More about Upper bounds and algorithms for parallel knock-out numbers.

The computational complexity of graph contractions II: two tough polynomially solvable cases (2008)
Journal Article
Levin, A., Paulusma, D., & Woeginger, G. (2008). The computational complexity of graph contractions II: two tough polynomially solvable cases. Networks, 52(1), 32-56. https://doi.org/10.1002/net.20249

For a fixed pattern graph H, let H-CONTRACTIBILITY denote the problem of deciding whether a given input graph is contractible to H. This article is part II of our study on the computational complexity of the H-CONTRACTIBILITY problem. In the first ar... Read More about The computational complexity of graph contractions II: two tough polynomially solvable cases.

The computational complexity of graph contractions I: polynomially solvable and NP-complete cases (2008)
Journal Article
Levin, A., Paulusma, D., & Woeginger, G. (2008). The computational complexity of graph contractions I: polynomially solvable and NP-complete cases. Networks, 51(3), 178-189. https://doi.org/10.1002/net.20214

For a fixed pattern graph H, let H-CONTRACTIBILITY denote the problem of deciding whether a given input graph is contractible to H. This paper is part I of our study on the computational complexity of the H-CONTRACTIBILITY problem. We continue a line... Read More about The computational complexity of graph contractions I: polynomially solvable and NP-complete cases.

Locally constrained graph homomorphisms and equitable partitions (2008)
Journal Article
Fiala, J., Paulusma, D., & Telle, J. (2008). Locally constrained graph homomorphisms and equitable partitions. European Journal of Combinatorics, 29(4), 850-880. https://doi.org/10.1016/j.ejc.2007.11.006

We explore the connection between locally constrained graph homomorphisms and degree matrices arising from an equitable partition of a graph. We provide several equivalent characterizations of degree matrices. As a consequence we can efficiently chec... Read More about Locally constrained graph homomorphisms and equitable partitions.

Relative length of longest paths and longest cycles in triangle-free graphs (2008)
Journal Article
Paulusma, D., & Yoshimoto, K. (2008). Relative length of longest paths and longest cycles in triangle-free graphs. Discrete Mathematics, 308(7), 1222-1229. https://doi.org/10.1016/j.disc.2007.03.070

In this paper, we study triangle-free graphs. Let G=(V,E) be an arbitrary triangle-free graph with minimum degree at least two and σ4(G)|V(G)|+2. We first show that either for any path P in G there exists a cycle C such that |VPVC|1, or G is isomorph... Read More about Relative length of longest paths and longest cycles in triangle-free graphs.

The computational complexity of the parallel knock-out problem (2008)
Journal Article
Broersma, H., Johnson, M., Paulusma, D., & Stewart, I. (2008). The computational complexity of the parallel knock-out problem. Theoretical Computer Science, 393(1-3), 182-195. https://doi.org/10.1016/j.tcs.2007.11.021

We consider computational complexity questions related to parallel knock-out schemes for graphs. In such schemes, in each round, each remaining vertex of a given graph eliminates exactly one of its neighbours. We show that the problem of whether, for... Read More about The computational complexity of the parallel knock-out problem.

A new algorithm for on-line coloring bipartite graphs (2008)
Journal Article
Broersma, H., Capponi, A., & Paulusma, D. (2008). A new algorithm for on-line coloring bipartite graphs. SIAM Journal on Discrete Mathematics, 22(1), 72-91. https://doi.org/10.1137/060668675

We first show that for any bipartite graph $H$ with at most five vertices there exists an on-line competitive algorithm for the class of $H$-free bipartite graphs. We then analyze the performance of an on-line algorithm for coloring bipartite graphs... Read More about A new algorithm for on-line coloring bipartite graphs.

On components of 2-factors in claw-free graphs (2007)
Journal Article
Broersma, H., Paulusma, D., & Yoshimoto, K. (2007). On components of 2-factors in claw-free graphs. Electronic Notes in Discrete Mathematics, 29, 289-293. https://doi.org/10.1016/j.endm.2007.07.050

For a non-hamiltonian claw-free graph G with order n and minimum degree δ we show the following. If δ=4, then G has a 2-factor with at most (5n−14)/18 components, unless G belongs to a finite class of exceptional graphs. If δ⩾5, then G has a 2-factor... Read More about On components of 2-factors in claw-free graphs.

Cycles through specified vertices in triangle-free graphs (2007)
Journal Article
Paulusma, D., & Yoshimito, K. (2007). Cycles through specified vertices in triangle-free graphs. Discussiones Mathematicae. Graph Theory, 27(1), 179-191. https://doi.org/10.7151/dmgt.1354

Let G be a triangle-free graph with δ(G) ≥ 2 and σ4(G) ≥ |V(G)|+2. Let S ⊂ V(G) consist of less than σ4/4+ 1 vertices. We prove the following. If all vertices of S have degree at least three, then there exists a cycle C containing S. Both the upper b... Read More about Cycles through specified vertices in triangle-free graphs.

A complete complexity classification of the role assignment problem (2005)
Journal Article
Fiala, J., & Paulusma, D. (2005). A complete complexity classification of the role assignment problem. Theoretical Computer Science, 349(1), 67-81. https://doi.org/10.1016/j.tcs.2005.09.029

In social network theory a society is often represented by a simple graph G, where vertices stand for individuals and edges represent relationships between those individuals. The description of the social network is tried to be simplified by assignin... Read More about A complete complexity classification of the role assignment problem.

The computational complexity of the elimination problem in generalized sports competitions (2004)
Journal Article
Kern, W., & Paulusma, D. (2004). The computational complexity of the elimination problem in generalized sports competitions. Discrete Optimization, 1(2), 205-214. https://doi.org/10.1016/j.disopt.2003.12.003

Consider a sports competition among various teams playing against each other in pairs (matches) according to a previously determined schedule. At some stage of the competition one may ask whether a particular team still has a (theoretical) chance to... Read More about The computational complexity of the elimination problem in generalized sports competitions.

Matching games : the least core and the nucleolus (2003)
Journal Article
Kern, W., & Paulusma, D. (2003). Matching games : the least core and the nucleolus. Mathematics of Operations Research, 28(2), 294-308. https://doi.org/10.1287/moor.28.2.294.14477

A matching game is a cooperative game defined by a graph G = (V, E). The player set is V and the value of a coalition S # V is defined as the size of a maximum matching in the subgraph induced by S. We show that the nucleolus of such games can be com... Read More about Matching games : the least core and the nucleolus.

Two extensions of the Shapley value for cooperative games (2001)
Journal Article
Driessen, T., & Paulusma, D. (2001). Two extensions of the Shapley value for cooperative games. Mathematical Methods of Operations Research, 53(1), 35-49. https://doi.org/10.1007/s001860000099

Two extensions of the Shapley value are given. First we consider a probabilistic framework in which certain consistent allocation rules such as the Shapley value are characterized. The second generalization of the Shapley value is an extension to the... Read More about Two extensions of the Shapley value for cooperative games.

The new FIFA rules are hard: complexity aspects of sports competitions (2001)
Journal Article
Kern, W., & Paulusma, D. (2001). The new FIFA rules are hard: complexity aspects of sports competitions. Discrete Applied Mathematics, 108(3), 317-323. https://doi.org/10.1016/s0166-218x%2800%2900241-9

Consider a soccer competition among various teams playing against each other in pairs (matches) according to a previously determined schedule. At some stage of the competition one may ask whether a particular team still has a (theoretical) chance to... Read More about The new FIFA rules are hard: complexity aspects of sports competitions.

Note on the computational complexity of least core concepts for min-cost spanning tree games (2000)
Journal Article
Faigle, U., Kern, W., & Paulusma, D. (2000). Note on the computational complexity of least core concepts for min-cost spanning tree games. Mathematical Methods of Operations Research, 52(1), 23-38. https://doi.org/10.1007/s001860000059

Various least core concepts including the classical least core of cooperative games are discussed. By a reduction from minimum cover problems, we prove that computing an element in these least cores is in general NP-hard for minimum cost spanning tre... Read More about Note on the computational complexity of least core concepts for min-cost spanning tree games.