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Characterizing face-number-related invariants of a given class simplicial complexes has been central topic in combinatorial topology. In this regard, one the well-known is g2. Let K be normal 3-pseudomanifold such that g2(K)≤g2(lk(v))+9 for some vertex v K. Suppose either only singularity or two singularities (at least) which an RP2-singularity. We prove obtained from boundary 4-simplices by se...
It is known that the list of excluded minors for the minor-closed class of graphs of path-width 6 3 numbers in the millions. However, if we restrict the class to 3-connected graphs of path-width 6 3, then we can characterize it by five excluded minors.
Contents 1 Complexity theory and an overview of the algorithm 3 1. 2 Surfaces and transverse surfaces in a spine 15 2.
A subgraph T of a graph G is a tree t-spanner of G if and only if T is a tree and for every pair of vertices in G their distance in T is at most t times their distance in G, where t is called a stretch factor of T . An efficient algorithm to determine whether a graph admits a tree 2-spanner has been developed, while for each t ≥ 4 the problem to determine whether a graph admits a tree t-spanner...
Acknowledgements My foremost thanks are to my supervisor Roman Nedela, for his continual encouragement, support and patience, for many inspirational conversations, leading me in the times of hasitations and careful reading many versions of the draft. Thanks also to Peter Maličk´y for the effort with some computations with groups and many advices in topology. Thanks also to Mathematical Institut...
A new combinatorial characterization of a gray-tone image called Euler Vector is proposed. Euler number of a binary image is a well-known topological feature, which remains invariant under translation, rotation, scaling, and rubber-sheet transformation of the image. Euler vector comprises of a 4-tuple, where each element is an integer representing the Euler number of the partial binary image fo...
Median filters and rank-order filters are generally considered to be more time consuming than, e.g., averaging filters. With the new algorithm presented in this report the opposite turns out to be true. The median (or any other rank-order value) is obtained by examining the bits of the arguments columnwise starting with the most significant bits. Hardware implementations suitable for parallel p...
Background Brazil is a country of Portuguese colonization with massive numbers of immigrants and Portuguese descendants (25 millions). At least half of all Brazilian Y chromosomes are from Portuguese origin. Nevertheless, this population suffered miscegenation with native Indians and African descendants. African descendants Brazilians have 48% of non-African genes, probably from Portuguese asce...
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