The generalized bull is the graph B(i,j) obtained by attaching endvertices of two disjoint paths of lengths i, j to two vertices of a triangle. We prove that every 3‐connected {K(1,3), X}‐free graph, where X ∈ {B(1,6), B(2,5),B(3,4)}, is Hamilton‐connected. The results are sharp&#x...

Aim: The aim of the presented work was to establish the success rate of spontaneous eruption of teeth (with incomplete roots development) with dentigerous (follicular) cyst into the mouth cavity after completed cystectomy. Further, the position of impacted teeth with obstacles represented&#x...

The weak and strong comparison principles (WCP and SCP, respectively) are investigated for quasilinear elliptic boundary value problems with the p-Laplacian in one space dimension, Δp(u) =d/dx(|u'|p−2u'). We treat the “degenerate” case of 2 <p <∞ and allow also for the non...

In this paper, we characterize all pairs of (possibly disconnected) graphs R, S such that (i) every 2‐connected {R, S}‐free graph of sufficiently large order has a 2‐factor, and (ii) every connected {R, S}‐free graph of sufficiently large order with minimum degree at least two...

We investigate automorphism groups of planar graphs. The main result is a complete recursive description of all abstract groups that can be realized as automorphism groups of planar graphs. The characterization is formulated in terms of inhomogeneous wreath products. In the proof, we&#x...

We derive conditions ensuring that the range of a set-valued mapping with a compact convex domain covers a prescribed set. In Fréchet spaces, we consider approximations by one single-valued mapping such that the inverse of it has convex fbers. Subsequently, in Banach and finite-dim...

We study existence of solutions for a boundary degenerate (or singular) quasilinear equation in a smooth bounded domain under Dirichlet boundary conditions. We consider a weighted p−Laplacian operator with a coefficient that is locally bounded inside the domain and satisfying certain additio...

We derive conditions ensuring that the range of a given continuous mapping with a compact convex domain covers a prescribed set. In Fréchet spaces, we consider approximations by one single-valued mapping such that the inverse of it has either convex fibers or admits a continuo...

We formulate a simple algorithm for computing global exact symmetries of closed discrete curves in the plane. The method is based on a suitable trigonometric interpolation of vertices of the given polyline and consequent computation of the symmetry group of the obtained trigonometric&#x...

We give a simple combinatorial description of an (n-2k+2)-chromatic edge-critical subgraph of the Schrijver graph SG(n,k), itself an induced vertex-critical subgraph of the Kneser graph KG(n,k). This extends the main result of Kaiser and Stehlík (2020) to all values of k, and sharpens&#...

A leaf matching operation on a graph consists of removing a vertex of degree 1 together with its neighbour from the graph. Let G be a d‐regular cyclically (d k − 1+2 )‐ edge‐connected graph of even order, where k ≥ 0 and d ≥ 3. We prove that for a...

We extend Szego--Weinberger type inequalities in various directions. We consider domains with holes with different type of symmetries as well as higher eigenvalues.

The class E(k) of hypergraphs with a k-exclusive sum labelling is hereditary, but non-trivial to characterise even for k=1. Our main result is a complete description of the minimal forbidden induced subhypergraphs of E(1) that are 3-uniform with maximum vertex degree 2. We also...

A fullerene graph is a 3-connected cubic planar graph with pentagonal and hexagonal faces. The leapfrog transformation of a planar graph produces the trucation of the dual of the given graph. A fullerene graph is leapfrog if it can be obtained from another fullerene graph ...

Edge-elimination is an operation of removing an edge of a cubic graph together with its endvertices and suppressing the resulting 2-valent vertices. We study the effect of this operation on the cyclic connectivity of a cubic graph. Disregarding a small number of cubic graphs w...

An improved convergence bound for the polynomially accelerated two-level method of Brousek et al. [Electron. Trans. Numer. Anal., 44 (2015), pp. 401–442, Section 5] is proven. This method is a reinterpretation of the smoothed aggregation method with an aggressive coarsening and massive ...

The presented paper studies the flow number F(G, σ) of flow-admissible signed graphs (G, σ) with two negative edges. We restrict our study to cubic graphs, because for each non-cubic signed graph (G, σ) there is a set of cubic graphs obtained from (G, σ) such that&#x...

This paper analyzes the structure of the set of positive solutions of a class of one-dimensional superlinear indefinite bvp’s. It is a paradigm of how mathematical analysis aids the numerical study of a problem,whereas simultaneously its numerical study confirms and illuminates the anal...

This paper deals with the Bayesian state estimation of nonlinear stochastic dynamic systems. The stress is laid on the numerical solution to the Chapman-Kolmogorov equation, which governs the prediction step of the point-mass filter and predictor, using the convolution. A novel density-weigh...

We provide algorithms to reconstruct rational ruled surfaces in three-dimensional projective space from the “apparent contour” of a single projection to the projective plane. We deal with the case of tangent developables and of general projections to of rational normal scrolls. In the&#...