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All Outputs (23)

Parameterized algorithms for finding square roots (2014)
Journal Article
Cochefert, M., Couturier, J., Golovach, P., & Paulusma, D. (2014). Parameterized algorithms for finding square roots. Algorithmica, https://doi.org/10.1007/s00453-014-9967-4

We show that the following two problems are fixed-parameter tractable with parameter k: testing whether a connected n-vertex graph with m edges has a square root with at most n−1+k edges and testing whether such a graph has a square root with at leas... Read More about Parameterized algorithms for finding square roots.

Linear-Time Algorithms for Scattering Number and Hamilton-Connectivity of Interval Graphs (2014)
Journal Article
Broersma, H., Fiala, J., Golovach, P., Kaiser, T., Paulusma, D., & Proskurowski, A. (2015). Linear-Time Algorithms for Scattering Number and Hamilton-Connectivity of Interval Graphs. Journal of Graph Theory, 79(4), 282-299. https://doi.org/10.1002/jgt.21832

We prove that for all inline image an interval graph is inline image-Hamilton-connected if and only if its scattering number is at most k. This complements a previously known fact that an interval graph has a nonnegative scattering number if and only... Read More about Linear-Time Algorithms for Scattering Number and Hamilton-Connectivity of Interval Graphs.

Closing complexity gaps for coloring problems on H-free graphs (2014)
Journal Article
Golovach, P., Paulusma, D., & Song, J. (2014). Closing complexity gaps for coloring problems on H-free graphs. Information and Computation, 237, 204-214. https://doi.org/10.1016/j.ic.2014.02.004

If a graph G contains no subgraph isomorphic to some graph H , then G is called H -free. A coloring of a graph G=(V,E) is a mapping c:V→{1,2,…} such that no two adjacent vertices have the same color, i.e., c(u)≠c(v) if uv∈E; if |c(V)|⩽k then c is a k... Read More about Closing complexity gaps for coloring problems on H-free graphs.

The computational complexity of disconnected cut and 2K2-partition (2014)
Journal Article
Martin, B., & Paulusma, D. (2015). The computational complexity of disconnected cut and 2K2-partition. Journal of Combinatorial Theory, Series B, 111, 17-37. https://doi.org/10.1016/j.jctb.2014.09.002

For a connected graph G=(V,E), a subset U⊆V is called a disconnected cut if U disconnects the graph and the subgraph induced by U is disconnected as well. We show that the problem to test whether a graph has a disconnected cut is NP-complete. This pr... Read More about The computational complexity of disconnected cut and 2K2-partition.

Graph editing to a fixed target (2014)
Journal Article
Golovach, P., Paulusma, D., & Stewart, I. (2017). Graph editing to a fixed target. Discrete Applied Mathematics, 216(Part 1), 181-190. https://doi.org/10.1016/j.dam.2014.07.008

For a fixed graph H, the H-Minor Edit problem takes as input a graph G and an integer k and asks whether G can be modified into H by a total of at most k edge contractions, edge deletions and vertex deletions. Replacing edge contractions by vertex di... Read More about Graph editing to a fixed target.

Detecting fixed patterns in chordal graphs in polynomial time (2014)
Journal Article
Belmonte, R., Golovach, P., Heggernes, P., van 't Hof, P., Kaminski, M., & Paulusma, D. (2014). Detecting fixed patterns in chordal graphs in polynomial time. Algorithmica, 69(3), 501-521. https://doi.org/10.1007/s00453-013-9748-5

The Contractibility problem takes as input two graphs G and H, and the task is to decide whether H can be obtained from G by a sequence of edge contractions. The Induced Minor and Induced Topological Minor problems are similar, but the first allows b... Read More about Detecting fixed patterns in chordal graphs in polynomial time.

Solutions for the stable roommates problem with payments (2014)
Journal Article
Biró, P., Bomhoff, M., Golovach, P., Kern, W., & Paulusma, D. (2014). Solutions for the stable roommates problem with payments. Theoretical Computer Science, 540-541, 53-61. https://doi.org/10.1016/j.tcs.2013.03.027

The stable roommates problem with payments has as input a graph G=(V,E)G=(V,E) with an edge weighting w:E→R≥0w:E→R≥0 and the problem is to find a stable solution. A solution is a matching MM with a vector p∈R≥0V that satisfies pu+pv=w(uv)pu+pv=w(uv)... Read More about Solutions for the stable roommates problem with payments.

Packing bipartite graphs with covers of complete bipartite graphs (2014)
Journal Article
Chalopin, J., & Paulusma, D. (2014). Packing bipartite graphs with covers of complete bipartite graphs. Discrete Applied Mathematics, 168, 40-50. https://doi.org/10.1016/j.dam.2012.08.026

For a set SS of graphs, a perfect SS-packing (SS-factor) of a graph GG is a set of mutually vertex-disjoint subgraphs of GG that each are isomorphic to a member of SS and that together contain all vertices of GG. If GG allows a covering (locally bije... Read More about Packing bipartite graphs with covers of complete bipartite graphs.

Coloring graphs without short cycles and long induced paths (2014)
Journal Article
Golovach, P., Paulusma, D., & Song, J. (2014). Coloring graphs without short cycles and long induced paths. Discrete Applied Mathematics, 167, 107-120. https://doi.org/10.1016/j.dam.2013.12.008

For an integer k≥1, a graph G is k-colorable if there exists a mapping c:VG→{1,…,k} such that c(u)≠c(v) whenever u and v are two adjacent vertices. For a fixed integer k≥1, the k-Coloring problem is that of testing whether a given graph is k-colorabl... Read More about Coloring graphs without short cycles and long induced paths.

List coloring in the absence of two subgraphs (2014)
Journal Article
Golovach, P., & Paulusma, D. (2014). List coloring in the absence of two subgraphs. Discrete Applied Mathematics, 166, 123-130. https://doi.org/10.1016/j.dam.2013.10.010

A list assignment of a graph G=(V,E) is a function L that assigns a list L(u) of so-called admissible colors to each u∈V. The List Coloring problem is that of testing whether a given graph G=(V,E) has a coloring c that respects a given list assignmen... Read More about List coloring in the absence of two subgraphs.

Colouring of graphs with Ramsey-type forbidden subgraphs (2014)
Journal Article
Dabrowski, K., Golovach, P., & Paulusma, D. (2014). Colouring of graphs with Ramsey-type forbidden subgraphs. Theoretical Computer Science, 522, 34-43. https://doi.org/10.1016/j.tcs.2013.12.004

A colouring of a graph G=(V,E) is a mapping c:V→{1,2,…} such that c(u)≠c(v) if uv∈E; if |c(V)|⩽k then c is a k -colouring. The Colouring problem is that of testing whether a given graph has a k -colouring for some given integer k . If a graph contain... Read More about Colouring of graphs with Ramsey-type forbidden subgraphs.

Obtaining Online Ecological Colourings by Generalizing First-Fit (2014)
Journal Article
Johnson, M., Patel, V., Paulusma, D., & Trunck, T. (2014). Obtaining Online Ecological Colourings by Generalizing First-Fit. Theory of Computing Systems, 54(2), 244-260. https://doi.org/10.1007/s00224-013-9513-9

A colouring of a graph is ecological if every pair of vertices that have the same set of colours in their neighbourhood are coloured alike. We consider the following problem: if a graph G and an ecological colouring c of G are given, can further vert... Read More about Obtaining Online Ecological Colourings by Generalizing First-Fit.

Knocking Out P_k-free Graphs (2014)
Conference Proceeding
Johnson, M., Paulusma, D., & Stewart, A. (2014). Knocking Out P_k-free Graphs. In E. Csuhaj-Varjú, M. Dietzfelbinger, & Z. Ésik (Eds.), 39th International Symposium, MFCS 2014, Budapest, Hungary, 26-29August 2014 ; proceedings, Part II (396-407). https://doi.org/10.1007/978-3-662-44465-8_34

A parallel knock-out scheme for a graph proceeds in rounds in each of which each surviving vertex eliminates one of its surviving neighbours. A graph is KO-reducible if there exists such a scheme that eliminates every vertex in the graph. The Paralle... Read More about Knocking Out P_k-free Graphs.

A Reconfigurations Analogue of Brooks’ Theorem (2014)
Conference Proceeding
Feghali, C., Johnson, M., & Paulusma, D. (2014). A Reconfigurations Analogue of Brooks’ Theorem. In E. Csuhaj-Varjú, M. Dietzfelbinger, & Z. Ésik (Eds.), 39th International Symposium, MFCS 2014, Budapest, Hungary, 26-29 August 2014 ; proceedings, Part II (287-298). https://doi.org/10.1007/978-3-662-44465-8_25

Let G be a simple undirected graph on n vertices with maximum degree Δ. Brooks’ Theorem states that G has a Δ-colouring unless G is a complete graph, or a cycle with an odd number of vertices. To recolour G is to obtain a new proper colouring by chan... Read More about A Reconfigurations Analogue of Brooks’ Theorem.

Editing to Eulerian Graphs (2014)
Conference Proceeding
Dabrowski, K. K., Golovach, P. A., Hof, V. P., & Paulusma, D. (2014). Editing to Eulerian Graphs. In V. Raman, & S. P. Suresh (Eds.), 34th International Conference on Foundation of Software Technology and Theoretical Computer Science (FSTTCS 2014) (97-108). https://doi.org/10.4230/lipics.fsttcs.2014.97

We investigate the problem of modifying a graph into a connected graph in which the degree of each vertex satisfies a prescribed parity constraint. Let ea, ed and vd denote the operations edge addition, edge deletion and vertex deletion respectively.... Read More about Editing to Eulerian Graphs.

Classifying the Clique-Width of H-Free Bipartite Graphs (2014)
Conference Proceeding
Dabrowski, K. K., & Paulusma, D. (2014). Classifying the Clique-Width of H-Free Bipartite Graphs. In Z. Cai, A. Zelikovsky, & A. G. Bourgeois (Eds.), 20th International Conference, COCOON 2014, Atlanta, GA, USA, 4-6 August 2014 ; proceedings (489-500). https://doi.org/10.1007/978-3-319-08783-2_42

Let G be a bipartite graph, and let H be a bipartite graph with a fixed bipartition (B H ,W H ). We consider three different, natural ways of forbidding H as an induced subgraph in G. First, G is H-free if it does not contain H as an induced subgraph... Read More about Classifying the Clique-Width of H-Free Bipartite Graphs.

Induced Disjoint Paths in Circular-Arc Graphs in Linear Time (2014)
Conference Proceeding
Golovach, P., Paulusma, D., & van Leeuwen, E. (2014). Induced Disjoint Paths in Circular-Arc Graphs in Linear Time. In 40th International Workshop, WG 2014, Nouan-le-Fuzelier, France, 25-27 June 2014 ; revised selected papers (225-237). https://doi.org/10.1007/978-3-319-12340-0_19

The Induced Disjoint Paths problem is to test whether a graph G with k distinct pairs of vertices (si,ti) contains paths P1,…,Pk such that Pi connects si and ti for i=1,…,k, and Pi and Pj have neither common vertices nor adjacent vertices (except per... Read More about Induced Disjoint Paths in Circular-Arc Graphs in Linear Time.

Narrowing the Complexity Gap for Colouring (C_s,P_t)-Free Graphs (2014)
Conference Proceeding
Huang, S., Johnson, M., & Paulusma, D. (2014). Narrowing the Complexity Gap for Colouring (C_s,P_t)-Free Graphs. In Q. Gu, P. Hell, & B. Yang (Eds.), 10th International Conference, AAIM 2014, Vancouver, BC, Canada, 8-11 July 2014 ; proceedings (162-173). https://doi.org/10.1007/978-3-319-07956-1_15

Let k be a positive integer. The k-Colouring problem is to decide whether a graph has a k-colouring. The k-Precolouring Extension problem is to decide whether a colouring of a subset of a graph’s vertex set can be extended to a k-colouring of the who... Read More about Narrowing the Complexity Gap for Colouring (C_s,P_t)-Free Graphs.