Choosability on H-free graphs (2013)
Journal Article
Golovach, P., Heggernes, P., van 't Hof, P., & Paulusma, D. (2013). Choosability on H-free graphs. Information Processing Letters, 113(4), 107-110. https://doi.org/10.1016/j.ipl.2012.12.003

A graph is H-free if it has no induced subgraph isomorphic to H. We determine the computational complexity of the Choosability problem restricted to H-free graphs for every graph H that does not belong to {K1,3,P1+P2,P1+P3,P4}{K1,3,P1+P2,P1+P3,P4}. W... Read More about Choosability on H-free graphs.

A note on contracting claw-free graphs (2013)
Journal Article
Fiala, J., Kaminski, M., & Paulusma, D. (2013). A note on contracting claw-free graphs. Discrete Mathematics & Theoretical Computer Science, 15(2), 223-232

A graph containment problem is to decide whether one graph called the host graph can be modified into some other graph called the target graph by using a number of specified graph operations. We consider edge deletions, edge contractions, vertex dele... Read More about A note on contracting claw-free graphs.

4-Coloring H-free graphs when H is small (2013)
Journal Article
Golovach, P., Paulusma, D., & Song, J. (2013). 4-Coloring H-free graphs when H is small. Discrete Applied Mathematics, 161(1-2), 140-150. https://doi.org/10.1016/j.dam.2012.08.022

The kk-Coloring problem is to test whether a graph can be colored with at most kk colors such that no two adjacent vertices receive the same color. If a graph GG does not contain a graph HH as an induced subgraph, then GG is called HH-free. For any f... Read More about 4-Coloring H-free graphs when H is small.

Exact algorithms for finding longest cycles in claw-free graphs (2013)
Journal Article
Broersma, H., Fomin, F., Hof van 't, P., & Paulusma, D. (2013). Exact algorithms for finding longest cycles in claw-free graphs. Algorithmica, 65(1), 129 -145. https://doi.org/10.1007/s00453-011-9576-4

The Hamiltonian Cycle problem is the problem of deciding whether an n-vertex graph G has a cycle passing through all vertices of G. This problem is a classic NP-complete problem. Finding an exact algorithm that solves it in O*(an)(n) time for some co... Read More about Exact algorithms for finding longest cycles in claw-free graphs.

Detecting induced star-like minors in polynomial time (2012)
Journal Article
Fiala, J., Kaminksi, M., & Paulusma, D. (2012). Detecting induced star-like minors in polynomial time. Journal of discrete algorithms, 17, 74-85. https://doi.org/10.1016/j.jda.2012.11.002

The Induced Minor problem is to test whether a graph G contains a graph H as an induced minor, i.e., if G can be modified into H by a sequence of vertex deletions and edge contractions. When H is fixed, i.e., not part of the input, this problem is de... Read More about Detecting induced star-like minors in polynomial time.

Computing vertex-surjective homomorphisms to partially reflexive trees (2012)
Journal Article
Golovach, P., Paulusma, D., & Song, J. (2012). Computing vertex-surjective homomorphisms to partially reflexive trees. Theoretical Computer Science, 457, 86-100. https://doi.org/10.1016/j.tcs.2012.06.039

A homomorphism from a graph GG to a graph HH is a vertex mapping f:VG→VHf:VG→VH such that f(u)f(u) and f(v)f(v) form an edge in HH whenever uu and vv form an edge in GG. The HH-Coloring problem is that of testing whether a graph GG allows a homomorph... Read More about Computing vertex-surjective homomorphisms to partially reflexive trees.

Finding vertex-surjective graph homomorphisms (2012)
Journal Article
Golovach, P., Lidicky, B., Martin, B., & Paulusma, D. (2012). Finding vertex-surjective graph homomorphisms. Acta Informatica, 49(6), 381-394. https://doi.org/10.1007/s00236-012-0164-0

The Surjective Homomorphism problem is to test whether a given graph G called the guest graph allows a vertex-surjective homomorphism to some other given graph H called the host graph. The bijective and injective homomorphism problems can be formulat... Read More about Finding vertex-surjective graph homomorphisms.

On the parameterized complexity of coloring graphs in the absence of a linear forest (2012)
Journal Article
Couturier, J., Golovach, P., Kratsch, D., & Paulusma, D. (2012). On the parameterized complexity of coloring graphs in the absence of a linear forest. Journal of discrete algorithms, 15, 56-62. https://doi.org/10.1016/j.jda.2012.04.008

The k-Coloring problem is to decide whether a graph can be colored with at most k colors such that no two adjacent vertices receive the same color. The Listk-Coloring problem requires in addition that every vertex u must receive a color from some giv... Read More about On the parameterized complexity of coloring graphs in the absence of a linear forest.

Computing role assignments of proper interval graphs in polynomial time (2012)
Journal Article
Heggernes, P., van 't Hof, P., & Paulusma, D. (2012). Computing role assignments of proper interval graphs in polynomial time. Journal of discrete algorithms, 14, 173-188. https://doi.org/10.1016/j.jda.2011.12.004

An R-role assignment of a graph G is a locally surjective homomorphism from G to graph R. For a fixed graph R, the R-Role Assignment problem is to decide, for an input graph G, whether G has an R-role assignment. When both graphs G and R are given as... Read More about Computing role assignments of proper interval graphs in polynomial time.

On graph contractions and induced minors (2012)
Journal Article
Hof, P. V. '., Kaminski, M., Paulusma, D., Szeider, S., & Thilikos, D. (2012). On graph contractions and induced minors. Discrete Applied Mathematics, 160(6), 799-809. https://doi.org/10.1016/j.dam.2010.05.005

The Induced Minor Containment problem takes as input two graphs G and H, and asks whether G has H as an induced minor. We show that this problem is fixed parameter tractable in |VH| if G belongs to any nontrivial minor-closed graph class and H is a p... Read More about On graph contractions and induced minors.

Distance three labelings of trees (2012)
Journal Article
Fiala, J., Golovach, P., Kratochvil, J., Lidický, B., & Paulusma, D. (2012). Distance three labelings of trees. Discrete Applied Mathematics, 160(6), 764-779. https://doi.org/10.1016/j.dam.2011.02.004

An L(2,1,1)-labeling of a graph G assigns nonnegative integers to the vertices of G in such a way that labels of adjacent vertices differ by at least two, while vertices that are at distance at most three are assigned different labels. The maximum la... Read More about Distance three labelings of trees.

Determining the chromatic number of triangle-free 2P3-free graphs in polynomial time (2012)
Journal Article
Broersma, H., Golovach, P., Paulusma, D., & Song, J. (2012). Determining the chromatic number of triangle-free 2P3-free graphs in polynomial time. Theoretical Computer Science, 423, 1-10. https://doi.org/10.1016/j.tcs.2011.12.076

Let 2P3 denote the disjoint union of two paths on three vertices. A graph G that has no subgraph isomorphic to a graph H is called H-free. The Vertex Coloring problem is the problem to determine the chromatic number of a graph. Its computational comp... Read More about Determining the chromatic number of triangle-free 2P3-free graphs in polynomial time.

Induced packing of odd cycles in planar graphs (2012)
Journal Article
Golovach, P., Kamiński, M., Paulusma, D., & Thilikos, D. (2012). Induced packing of odd cycles in planar graphs. Theoretical Computer Science, 420, 28-35. https://doi.org/10.1016/j.tcs.2011.11.004

An induced packing of odd cycles in a graph is a packing such that there is no edge in the graph between any two odd cycles in the packing. We prove that an induced packing of k odd cycles in an n-vertex graph can be found (if it exists) in time 2O(k... Read More about Induced packing of odd cycles in planar graphs.

The k-in-a-path problem for claw-free graphs (2012)
Journal Article
Fiala, J., Kamiński, M., Lidický, B., & Paulusma, D. (2012). The k-in-a-path problem for claw-free graphs. Algorithmica, 62(1-2), 499-519. https://doi.org/10.1007/s00453-010-9468-z

The k-in-a-Path problem is to test whether a graph contains an induced path spanning k given vertices. This problem is NP-complete in general graphs, already when k=3. We show how to solve it in polynomial time on claw-free graphs, when k is an arbit... Read More about The k-in-a-path problem for claw-free graphs.

Finding induced paths of given parity in claw-free graphs (2012)
Journal Article
Hof van 't, P., Kamiński, M., & Paulusma, D. (2012). Finding induced paths of given parity in claw-free graphs. Algorithmica, 62(1-2), 537-563. https://doi.org/10.1007/s00453-010-9470-5

The Parity Path problem is to decide if a given graph contains both an induced path of odd length and an induced path of even length between two specified vertices. In the related problems Odd Induced Path and Even Induced Path, the goal is to determ... Read More about Finding induced paths of given parity in claw-free graphs.

Updating the complexity status of coloring graphs without a fixed induced linear forest (2012)
Journal Article
Broersma, H., Golovach, P., Paulusma, D., & Song, J. (2012). Updating the complexity status of coloring graphs without a fixed induced linear forest. Theoretical Computer Science, 414(1), 9-19. https://doi.org/10.1016/j.tcs.2011.10.005

A graph is H-free if it does not contain an induced subgraph isomorphic to the graph H. The graph Pk denotes a path on k vertices. The ℓ-Coloring problem is the problem to decide whether a graph can be colored with at most ℓ colors such that adjacent... Read More about Updating the complexity status of coloring graphs without a fixed induced linear forest.

Computing solutions for matching games (2012)
Journal Article
Biro, P., Kern, W., & Paulusma, D. (2012). Computing solutions for matching games. International Journal of Game Theory, 41(1), 75-90. https://doi.org/10.1007/s00182-011-0273-y

A matching game is a cooperative game (N, v) defined on a graph G = (N, E) with an edge weighting w: E® \mathbb R+w:ER+. The player set is N and the value of a coalition S Í NSN is defined as the maximum weight of a matching in the subgraph induced b... Read More about Computing solutions for matching games.

Containment relations in split graphs (2012)
Journal Article
Golovach, P., Kaminski, M., Paulusma, D., & Thilikos, D. (2012). Containment relations in split graphs. Discrete Applied Mathematics, 160(1-2), 155-163. https://doi.org/10.1016/j.dam.2011.10.004

A graph containment problem is to decide whether one graph can be modified into some other graph by using a number of specified graph operations. We consider edge deletions, edge contractions, vertex deletions and vertex dissolutions as possible grap... Read More about Containment relations in split graphs.

Lift Contractions (2011)
Journal Article
Golovach, P., Kamiński, M., Paulusma, D., & Thilikos, D. (2011). Lift Contractions. Electronic Notes in Discrete Mathematics, 38(1), 407-412. https://doi.org/10.1016/j.endm.2011.09.066

We introduce and study a new containment relation in graphs – lift contractions. H is a lift contraction of G if H can be obtained from G by a sequence of edge lifts and edge contractions. We show that a graph contains every n-vertex graph as a lift... Read More about Lift Contractions.

On the diameter of reconfiguration graphs for vertex colourings (2011)
Journal Article
Bonamy, M., Johnson, M., Lignos, I., Patel, V., & Paulusma, D. (2011). On the diameter of reconfiguration graphs for vertex colourings. Electronic Notes in Discrete Mathematics, 38(1), 161-166. https://doi.org/10.1016/j.endm.2011.09.028

The reconfiguration graph of the k-colourings of a graph G contains as its vertex set the proper vertex k-colourings of G, and two colourings are joined by an edge in the reconfiguration graph if they differ in colour on just one vertex of G. We prov... Read More about On the diameter of reconfiguration graphs for vertex colourings.