Polynomial kernelization for removing induced claws and diamonds

A graph is called (claw,diamond)-free if it contains neither a claw (a $K_{1,3}$) nor a diamond (a $K_4$ with an edge removed) as an induced subgraph. Equivalently, (claw,diamond)-free graphs can be characterized as line graphs of triangle-free graphs, or as linear dominoes, i.e., graphs in which every vertex is in at most two maximal cliques and every edge is in exactly one maximal clique. In this paper we consider the parameterized complexity of the (claw,diamond)-free Edge Deletion problem, where given a graph $G$ and a parameter $k$, the question is whether one can remove at most $k$ edges from $G$ to obtain a (claw,diamond)-free graph. Our main result is that this problem admits a polynomial kernel. We complement this finding by proving that, even on instances with maximum degree $6$, the problem is NP-complete and cannot be solved in time $2^{o(k)}\cdot |V(G)|^{O(1)}$ unless the Exponential Time Hypothesis fai

Maximizing Happiness in Graphs of Bounded Clique-Width

Clique-width is one of the most important parameters that describes structural complexity of a graph. Probably, only treewidth is more studied graph width parameter. In this paper we study how clique-width influences the complexity of the Maximum Happy Vertices (MHV) and Maximum Happy Edges (MHE) problems. We answer a question of Choudhari and Reddy '18 about parameterization by the distance to threshold graphs by showing that MHE is NP-complete on threshold graphs. Hence, it is not even in XP when parameterized by clique-width, since threshold graphs have clique-width at most two. As a complement for this result we provide a $n^{\mathcal{O}(\ell \cdot \operatorname{cw})}$ algorithm for MHE, where $\ell$ is the number of colors and $\operatorname{cw}$ is the clique-width of the input graph. We also construct an FPT algorithm for MHV with running time $\mathcal{O}^*((\ell+1)^{\mathcal{O}(\operatorname{cw})})$, where $\ell$ is the number of colors in the input. Additionally, we show $\mathcal{O}(\ell n^2)$ algorithm for MHV on interval graphs.Comment: Accepted to LATIN 202

Post-traumatic pelvic deformity with old injuries of rectum and urogenital tract: 18-year follow-up

The authors described a case of management the severe combined pelvis trauma in female patient with 18 years follow-up. At the age of seven, the patient was injured: the open vertical unstable pelvis injury with severe damage of urogenital tract and rectum. Numerous operations on the pelvic organs without surgical treatment of pelvic ring fractures were accompanied by complications. At the age of 21 (14 years later) the patient was subjected to the surgery according to the techniques designed in the Chaklin Ural Scientific Research Institute of Traumatology and Orthopaedics: percutaneous osteotomy of posterior and anterior pelvis, external pelvis fixation using circular device with a further gradual (within 1.5 months) correction of the deformity with apparatus and subsequent internal fixation with screws. There were achieved partially elimination of shortening of the right lower limb, correction of the pelvic ring form, increasing the pelvic cavity volume, elimination of vaginal impingement, that allowed to correct urological problems with the possibility of further recovery of the vagina and hip replacement surgery. This case showed that the management of patients with complicated pelvis injuries required a multidisciplinary approach: emergency fixation of the unstable injuries and application of techniques to correct long-standing pelvis deformities to restore stability and shape of the pelvic ring, which created the more favorable conditions for reconstructive surgery of the pelvic organs

GENETIC FACTORS OF MALE INFERTILITY, THEIR COMBINATIONS AND THE SPERMATOLOGICAL CHARACTERISTICS OF MEN WITH FERTILITY FAILURES

The objective is to study the occurrence of common genetic factors of male infertility in men with reproductive problems, their combinations and spermatological characteristics.Materials and methods. 393 men with infertility in marriage were examined. According to the results of the cytogenetic study, the sample is divided into 3 groups: 135 men with numerical sex chromosome abnormalities; 58 male patients with a balanced structural rearrangement; 200 men with normal karyotype. Y chromosome microdeletions, CFTR gene mutations and CAG-repeats polymorphism of AR gene were analyzed.Results. The Y-chromosome microdeletions partially AZFc deletions were detected in 13 % male patients with sex chromosome abnormalities. A combination of chromosomal abnormalities with AZF deletions and/or CFTR gene mutations and long CAG repeats of AR gene was found in 19 % infertile men with balanced chromosome rearrangements. Infertile men with normal male karyotype presented the frequency of common genetic factors of male infertility was almost 2 times higher than the combined frequency of these factors in groups of patients with chromosomes abnormalities. Azoospermia in men with normal karyotype and patients with chromosome abnormalities was diagnosed with the same frequency (58 %). In all men who have identified the presence of two or more genetic factors of male infertility, severe forms of pathozoospermia (azoospermia and severe oligozoospermia) were found.Conclusion. The combination of genetic factors of male infertility is accompanied by severe forms of pathozoospermia that indicates a possible additive effect of negative effect on spermatogenesis and male fertility