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On partitioning a graph into two connected subgraphs (2011)
Journal Article
Paulusma, D., & Rooij van, J. (2011). On partitioning a graph into two connected subgraphs. Theoretical Computer Science, 412(48), 6761-6769. https://doi.org/10.1016/j.tcs.2011.09.001

Suppose a graph G is given with two vertex-disjoint sets of vertices Z1 and Z2. Can we partition the remaining vertices of G such that we obtain two connected vertex-disjoint subgraphs of G that contain Z1 and Z2, respectively? This problem is known... Read More about On partitioning a graph into two connected subgraphs.

The longest path problem has a polynomial solution on interval graphs (2011)
Journal Article
Ioannidou, K., Mertzios, G., & Nikolopoulos, S. (2011). The longest path problem has a polynomial solution on interval graphs. Algorithmica, 61(2), 320-341. https://doi.org/10.1007/s00453-010-9411-3

The longest path problem is the problem of finding a path of maximum length in a graph. Polynomial solutions for this problem are known only for small classes of graphs, while it is NP-hard on general graphs, as it is a generalization of the Hamilton... Read More about The longest path problem has a polynomial solution on interval graphs.

Parameterizing cut sets in a graph by the number of their components (2011)
Journal Article
Ito, T., Kaminski, M., Paulusma, D., & Thilikos, D. (2011). Parameterizing cut sets in a graph by the number of their components. Theoretical Computer Science, 412(45), 6340-6350. https://doi.org/10.1016/j.tcs.2011.07.005

For a connected graph G=(V,E), a subset U⊆V is a disconnected cut if U disconnects G and the subgraph G[U] induced by U is disconnected as well. A cut U is a k-cut if G[U] contains exactly k(≥1) components. More specifically, a k-cut U is a (k,ℓ)-cut... Read More about Parameterizing cut sets in a graph by the number of their components.

Bipancyclicity in k-ary n-cubes with faulty edges under a conditional fault assumption (2011)
Journal Article
Xiang, Y., & Stewart, I. (2011). Bipancyclicity in k-ary n-cubes with faulty edges under a conditional fault assumption. IEEE Transactions on Parallel and Distributed Systems, 22(9), 1506-1513. https://doi.org/10.1109/tpds.2011.22

We prove that a k-ary 2-cube Q^k_2 with 3 faulty edges but where every vertex is incident with at least 2 healthy edges is bipancyclic, if k \geq 3, and k-pancyclic, if k \geq 5 is odd (these results are optimal). We go on to show that when k \geq 4... Read More about Bipancyclicity in k-ary n-cubes with faulty edges under a conditional fault assumption.

The recognition of tolerance and bounded tolerance graphs (2011)
Journal Article
Mertzios, G., Sau, I., & Zaks, S. (2011). The recognition of tolerance and bounded tolerance graphs. SIAM Journal on Computing, 40(5), 1234-1257. https://doi.org/10.1137/090780328

Tolerance graphs model interval relations in such a way that intervals can tolerate a certain degree of overlap without being in conflict. This subclass of perfect graphs has been extensively studied, due to both its interesting structure and its num... Read More about The recognition of tolerance and bounded tolerance graphs.