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Fast Exact Algorithms for Hamiltonicity in Claw-Free Graphs (2009)
Presentation / Conference Contribution
Broersma, H. J., Fomin, F. V., Hof van 't, P., & Paulusma, D. (2009, June). Fast Exact Algorithms for Hamiltonicity in Claw-Free Graphs. Presented at 35th International Workshop on Graph-Theoretic Concepts in Computer Science (WG 2009), Montpellier, France

The Hamiltonian Cycle problem asks if an n-vertex graph G has a cycle passing through all vertices of G. This problem is a classic NP-complete problem. So far, finding an exact algorithm that solves it in O *(α n ) time for some constant α< 2 is a no...

Sharp upper bounds for the minimum number of components of 2-factors in claw-free graphs (2009)
Journal Article
Broersma, H., Paulusma, D., & Yoshimoto, K. (2009). Sharp upper bounds for the minimum number of components of 2-factors in claw-free graphs. Graphs and Combinatorics, 25(4), 427-460. https://doi.org/10.1007/s00373-009-0855-7

Let G be a claw-free graph with order n and minimum degree δ. We improve results of Faudree et al. and Gould & Jacobson, and solve two open problems by proving the following two results. If δ = 4, then G has a 2-factor with at most (5n − 14)/18 compo... Read More about Sharp upper bounds for the minimum number of components of 2-factors in claw-free graphs.

Three complexity results on coloring Pk-free graphs (2009)
Presentation / Conference Contribution
Broersma, H. J., Fomin, F. V., Golovach, P. A., & Paulusma, D. (2023, June). Three complexity results on coloring Pk-free graphs. Presented at 20th International Workshop on Combinatorial Algorithms (IWOCA 2009), Hradec nad Moravicí, Czech Republic

We prove three complexity results on vertex coloring problems restricted to Pk-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 rema... Read More about Three complexity results on coloring Pk-free graphs.

Fully decomposable split graphs (2009)
Presentation / Conference Contribution
Broersma, H., Kratsch, D., & Woeginger, G. (2023, June). Fully decomposable split graphs. Presented at 20th International Workshop on Combinatorial Algorithms (IWOCA 2009), Hradec nad Moravicí, Czech Republic

We discuss various questions around partitioning a split graph into connected parts. Our main result is a polynomial time algorithm that decides whether a given split graph is fully decomposable, i.e., whether it can be partitioned into connected par... Read More about Fully decomposable split graphs.

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.

On hamiltonicity of P3-dominated graphs (2009)
Journal Article
Broersma, H., & Vumar, E. (2009). On hamiltonicity of P3-dominated graphs. Mathematical Methods of Operations Research, 69(2), 297-306. https://doi.org/10.1007/s00186-008-0260-7

We introduce a new class of graphs which we call P₃-dominated graphs. This class properly contains all quasi-claw-free graphs, and hence all claw-free graphs. Let G be a 2-connected P₃-dominated graph. We prove that G is hamiltonian if α(G²) ≤ κ(G),... Read More about On hamiltonicity of P3-dominated graphs.

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.

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.

On-line coloring of H-free bipartite graphs. (2006)
Presentation / Conference Contribution
Broersma, H. J., Capponi, A., & Paulusma, D. (2006, May). On-line coloring of H-free bipartite graphs. Presented at 6th Italian Conference on Algorithms and Complexity (CIAC 2006)., Rome, Italy

We present a new on-line algorithm for coloring bipartite graphs. This yields a new upper bound on the on-line chromatic number of bipartite graphs, improving a bound due to Lovász, Saks and Trotter. The algorithm is on-line competitive on various cl... Read More about On-line coloring of H-free bipartite graphs..

Planar graph coloring avoiding monochromatic subgraphs : trees and paths make it difficult (2006)
Journal Article
Broersma, H., Fomin, F., Kratochvil, J., & Woeginger, G. (2006). Planar graph coloring avoiding monochromatic subgraphs : trees and paths make it difficult. Algorithmica, 44(4), 343-361. https://doi.org/10.1007/s00453-005-1176-8

We consider the problem of coloring a planar graph with the minimum number of colors so that each color class avoids one or more forbidden graphs as subgraphs. We perform a detailed study of the computational complexity of this problem. We present a... Read More about Planar graph coloring avoiding monochromatic subgraphs : trees and paths make it difficult.

Global connectivity and expansion : long cycles and factors in f-connected graphs (2006)
Journal Article
Brandt, S., Broersma, H., Diestel, R., & Kriesell, M. (2006). Global connectivity and expansion : long cycles and factors in f-connected graphs. Combinatorica, 26(1), 17-36. https://doi.org/10.1007/s00493-006-0002-5

Given a function f : N → R, call an n-vertex graph f-connected if separating off k vertices requires the deletion of at least f(k) vertices whenever k ≤ (n−f(k))/2. This is a common generalization of vertex connectivity (when f is constant) and expan... Read More about Global connectivity and expansion : long cycles and factors in f-connected graphs.

The computational complexity of the parallel knock-out problem (2006)
Presentation / Conference Contribution
Broersma, H., Johnson, M., Paulusma, D., & Stewart, I. (2006, March). The computational complexity of the parallel knock-out problem. Presented at 7th Latin American Theoretical Informatics Symposium (LATIN 2006), Valdivia, Chile

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.

Radio labeling with preassigned frequencies (2004)
Journal Article
Bodlaender, H., Broersma, H., Fomin, F., Pyatkin, A., & Woeginger, G. (2004). Radio labeling with preassigned frequencies. SIAM Journal on Optimization, 15(1), 1-16. https://doi.org/10.1137/s1052623402410181

A radio labeling of a graph G is an assignment of pairwise distinct, positive integer labels to the vertices of G such that labels of adjacent vertices differ by at least $2$. The radio labeling problem (RL) consists in determining a radio labeling t... Read More about Radio labeling with preassigned frequencies.