Maximal induced matchings in triangle-free graphs

An induced matching in a graph is a set of edges whose endpoints induce a $1$-regular subgraph. It is known that any $n$-vertex graph has at most $10^{n/5} \approx 1.5849^n$ maximal induced matchings, and this bound is best possible. We prove that any $n$-vertex triangle-free graph has at most $3^{n/3} \approx 1.4423^n$ maximal induced matchings, and this bound is attained by any disjoint union of copies of the complete bipartite graph $K_{3,3}$. Our result implies that all maximal induced matchings in an $n$-vertex triangle-free graph can be listed in time $O(1.4423^n)$, yielding the fastest known algorithm for finding a maximum induced matching in a triangle-free graph.Comment: 17 page

Mod/Resc Parsimony Inference

We address in this paper a new computational biology problem that aims at understanding a mechanism that could potentially be used to genetically manipulate natural insect populations infected by inherited, intra-cellular parasitic bacteria. In this problem, that we denote by \textsc{Mod/Resc Parsimony Inference}, we are given a boolean matrix and the goal is to find two other boolean matrices with a minimum number of columns such that an appropriately defined operation on these matrices gives back the input. We show that this is formally equivalent to the \textsc{Bipartite Biclique Edge Cover} problem and derive some complexity results for our problem using this equivalence. We provide a new, fixed-parameter tractability approach for solving both that slightly improves upon a previously published algorithm for the \textsc{Bipartite Biclique Edge Cover}. Finally, we present experimental results where we applied some of our techniques to a real-life data set.Comment: 11 pages, 3 figure

Chiral three-nucleon forces and bound excited states in neutron-rich oxygen isotopes

We study the spectra of neutron-rich oxygen isotopes based on chiral two- and three-nucleon interactions. First, we benchmark our many-body approach by comparing ground-state energies to coupled-cluster results for the same two-nucleon interaction, with overall good agreement. We then calculate bound excited states in 21,22,23O, focusing on the role of three-nucleon forces, in the standard sd shell and an extended sdf7/2p3/2 valence space. Chiral three-nucleon forces provide important one- and two-body contributions between valence neutrons. We find that both these contributions and an extended valence space are necessary to reproduce key signatures of novel shell evolution, such as the N = 14 magic number and the low-lying states in 21O and 23O, which are too compressed with two-nucleon interactions only. For the extended space calculations, this presents first work based on nuclear forces without adjustments. Future work is needed and open questions are discussed.Comment: 6 pages, 4 figures, published versio

Reconfiguration of Cliques in a Graph

We study reconfiguration problems for cliques in a graph, which determine whether there exists a sequence of cliques that transforms a given clique into another one in a step-by-step fashion. As one step of a transformation, we consider three different types of rules, which are defined and studied in reconfiguration problems for independent sets. We first prove that all the three rules are equivalent in cliques. We then show that the problems are PSPACE-complete for perfect graphs, while we give polynomial-time algorithms for several classes of graphs, such as even-hole-free graphs and cographs. In particular, the shortest variant, which computes the shortest length of a desired sequence, can be solved in polynomial time for chordal graphs, bipartite graphs, planar graphs, and bounded treewidth graphs

Feedback Vertex Sets in Tournaments

We study combinatorial and algorithmic questions around minimal feedback vertex sets in tournament graphs. On the combinatorial side, we derive strong upper and lower bounds on the maximum number of minimal feedback vertex sets in an n-vertex tournament. We prove that every tournament on n vertices has at most 1.6740^n minimal feedback vertex sets, and that there is an infinite family of tournaments, all having at least 1.5448^n minimal feedback vertex sets. This improves and extends the bounds of Moon (1971). On the algorithmic side, we design the first polynomial space algorithm that enumerates the minimal feedback vertex sets of a tournament with polynomial delay. The combination of our results yields the fastest known algorithm for finding a minimum size feedback vertex set in a tournament

On cycle transversals and their connected variants in the absence of a small linear forest.

A graph is H-free if it contains no induced subgraph isomorphic to H. We prove new complexity results for the two classical cycle transversal problems Feedback Vertex Set and Odd Cycle Transversal by showing that they can be solved in polynomial time for (sP1+P3) -free graphs for every integer s≥1 . We show the same result for the variants Connected Feedback Vertex Set and Connected Odd Cycle Transversal. For the latter two problems we also prove that they are polynomial-time solvable for cographs; this was known already for Feedback Vertex Set and Odd Cycle Transversal

Occlusal adjustment using the bite plate-induced occlusal position as a reference position for temporomandibular disorders: a pilot study

<p>Abstract</p> <p>Background</p> <p>Many researchers have not accepted the use of occlusal treatments for temporomandibular disorders (TMDs). However, a recent report described a discrepancy between the habitual occlusal position (HOP) and the bite plate-induced occlusal position (BPOP) and discussed the relation of this discrepancy to TMD. Therefore, the treatment outcome of evidence-based occlusal adjustments using the bite plate-induced occlusal position (BPOP) as a muscular reference position should be evaluated in patients with TMD.</p> <p>Methods</p> <p>The BPOP was defined as the position at which a patient voluntarily closed his or her mouth while sitting in an upright posture after wearing an anterior flat bite plate for 5 minutes and then removing the plate. Twenty-one patients with TMDs underwent occlusal adjustment using the BPOP. The occlusal adjustments were continued until bilateral occlusal contacts were obtained in the BPOP. The treatment outcomes were evaluated using the subjective dysfunction index (SDI) and the Helkimo Clinical Dysfunction Index (CDI) before and after the occlusal adjustments; the changes in these two indices between the first examination and a one-year follow-up examination were then analyzed. In addition, the difference between the HOP and the BPOP was three-dimensionally measured before and after the treatment.</p> <p>Results</p> <p>The percentage of symptom-free patients after treatment was 86% according to the SDI and 76% according to the CDI. The changes in the two indices after treatment were significant (p < 0.001). The changes in the mean HOP-BPOP differences on the x-axis (mediolateral) and the y-axis (anteroposterior) were significant (p < 0.05), whereas the change on the z-axis (superoinferior) was not significant (p > 0.1).</p> <p>Conclusion</p> <p>Although the results of the present study should be confirmed in other studies, a randomized clinical trial examining occlusal adjustments using the BPOP as a reference position appears to be warranted.</p

Listing Maximal Independent Sets with Minimal Space and Bounded Delay

International audienceAn independent set is a set of nodes in a graph such that no two of them are adjacent. It is maximal if there is no node outside the independent set that may join it. Listing maximal independent sets in graphs can be applied, for example, to sample nodes belonging to different communities or clusters in network analysis and document clustering. The problem has a rich history as it is related to maximal cliques, dominance sets, vertex covers and 3-colorings in graphs. We are interested in reducing the delay, which is the worst-case time between any two consecutively output solutions, and the memory footprint, which is the additional working space behind the read-only input graph