Algorithms for square-3PC(·, ·)-free Berge graphs

We consider the class of graphs containing no odd hole, no odd antihole, and no configuration consisting of three paths between two nodes such that any two of the paths induce a hole, and at least two of the paths are of length 2. This class generalizes clawfree Berge graphs and square-free Berge graphs. We give a combinatorial algorithm of complexity O(n7) to find a clique of maximum weight in such a graph. We also consider several subgraph-detection problems related to this class

A polynomial Turing-kernel for weighted independent set in bull-free graphs

The maximum stable set problem is NP-hard, even when restricted to triangle-free graphs. In particular, one cannot expect a polynomial time algorithm deciding if a bull-free graph has a stable set of size k, when k is part of the instance. Our main result in this paper is to show the existence of an FPT algorithm when we parameterize the problem by the solution size k. A polynomial kernel is unlikely to exist for this problem. We show however that our problem has a polynomial size Turingkernel. More precisely, the hard cases are instances of size O(k5). As a byproduct, if we forbid odd holes in addition to the bull, we show the existence of a polynomial time algorithm for the stable set problem. We also prove that the chromatic number of a bull-free graph is bounded by a function of its clique number and the maximum chromatic number of its triangle-free induced subgraphs. All our results rely on a decomposition theorem for bull-free graphs due to Chudnovsky which is modified here, allowing us to provide extreme decompositions, adapted to our computational purpose

A polynomial Turing-kernel for weighted independent set in bull-free graphs

The maximum stable set problem is NP-hard, even when restricted to triangle-free graphs. In particular, one cannot expect a polynomial time algorithm deciding if a bull-free graph has a stable set of size k, when k is part of the instance. Our main result in this paper is to show the existence of an FPT algorithm when we parameterize the problem by the solution size k. A polynomial kernel is unlikely to exist for this problem. We show however that our problem has a polynomial size Turingkernel. More precisely, the hard cases are instances of size O(k5). As a byproduct, if we forbid odd holes in addition to the bull, we show the existence of a polynomial time algorithm for the stable set problem. We also prove that the chromatic number of a bull-free graph is bounded by a function of its clique number and the maximum chromatic number of its triangle-free induced subgraphs. All our results rely on a decomposition theorem for bull-free graphs due to Chudnovsky which is modified here, allowing us to provide extreme decompositions, adapted to our computational purpose

Stable Sets in {ISK₄,wheel}-Free Graphs

An ISK4 in a graph G is an induced subgraph of G that is isomorphic to a subdivision of K₄ (the complete graph on four vertices). A wheel is a graph that consists of a chordless cycle, together with a vertex that has at least three neighbors in the cycle. A graph is {ISK₄,wheel}-free if it has no ISK₄ and does not contain a wheel as an induced subgraph. We give an O(|V(G)|⁷)-time algorithm to compute the maximum weight of a stable set in an input weighted {ISK₄,wheel}-free graph G with non-negative integer weights

On rank-width of even-hole-free graphs

We present a class of (diamond, even hole)-free graphs with no clique cutset that has unbounded rank-width. In general, even-hole-free graphs have unbounded rank-width, because chordal graphs are even-hole-free. A. A. da Silva, A. Silva and C. Linhares-Sales (2010) showed that planar even-hole-free graphs have bounded rank-width, and N. K. Le (2016) showed that even-hole-free graphs with no star cutset have bounded rank width. A natural question is to ask, whether even-hole-free graphs with no clique cutsets have bounded rank-width. Our result gives a negative answer. Hence we cannot apply the meta-theorem by Courcelle, Makowsky and Rotics, which would provide efficient algorithms for a large number of problems, including the maximum independent set problem, whose complexity remains open for (diamond, even hole)-free graphs

Solar cycle variations of the Cluster spacecraft potential and its use for electron density estimations

International audience[1] A sunlit conductive spacecraft, immersed in tenuous plasma, will attain a positive potential relative to the ambient plasma. This potential is primarily governed by solar irradiation, which causes escape of photoelectrons from the surface of the spacecraft, and the electrons in the ambient plasma providing the return current. In this paper we combine potential measurements from the Cluster satellites with measurements of extreme ultraviolet radiation from the TIMED satellite to establish a relation between solar radiation and spacecraft charging from solar maximum to solar minimum. We then use this relation to derive an improved method for determination of the current balance of the spacecraft. By calibration with other instruments we thereafter derive the plasma density. The results show that this method can provide information about plasma densities in the polar cap and magnetotail lobe regions where other measurements have limitations

Triangle-free graphs that do not contain an induced subdivision of K₄ are 3-colorable

We show that triangle-free graphs that do not contain an induced subgraph isomorphic to a subdivision of K4 are 3-colorable. This proves a conjecture of Trotignon and Vušković [J. Graph Theory. 84 (2017), no. 3, pp. 233–248]

Trimetric Imaging of the Martian Ionosphere Using a CubeSat Constellation

Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/143020/1/6.2017-5252.pd

Coloring square-free Berge graphs

We consider the class of Berge graphs that do not contain an induced cycle of length four. We present a purely graph-theoretical algorithm that produces an optimal coloring in polynomial time for every graph in that class

Graphs with polynomially many minimal separators

We show that graphs that do not contain a theta, pyramid, prism, or turtle as an induced subgraph have polynomially many minimal separators. This result is the best possible in the sense that there are graphs with exponentially many minimal separators if only three of the four induced subgraphs are excluded. As a consequence, there is a polynomial time algorithm to solve the maximum weight independent set problem for the class of (theta, pyramid, prism, turtle)-free graphs. Since every prism, theta, and turtle contains an even hole, this also implies a polynomial time algorithm to solve the maximum weight independent set problem for the class of (pyramid, even hole)-free graphs