منابع مشابه
Finite groups have even more centralizers
For a finite group $G$, let $Cent(G)$ denote the set of centralizers of single elements of $G$. In this note we prove that if $|G|leq frac{3}{2}|Cent(G)|$ and $G$ is 2-nilpotent, then $Gcong S_3, D_{10}$ or $S_3times S_3$. This result gives a partial and positive answer to a conjecture raised by A. R. Ashrafi [On finite groups with a given number of centralizers, Algebra Collo...
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We describe efficient algorithms for finding even cycles in undirected graphs. Our main results are the following: (i) For every k ≥ 2, there is an O(V ) time algorithm that decides whether an undirected graph G = (V,E) contains a simple cycle of length 2k and finds one if it does. (ii) There is an O(V ) time algorithm that finds a shortest even cycle in an undirected graph G = (V,E).
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Problems of the following kind have been the focus of much recent research in the realm of parameterized complexity: Given an input graph (digraph) on n vertices and a positive integer parameter k, find if there exist k edges (arcs) whose deletion results in a graph that satisfies some specified parity constraints. In particular, when the objective is to obtain a connected graph in which all th...
متن کاملOn Even and Harmonic-Even Partial Cubes
Fukuda and Handa [7] asked whether every even partial cube G is harmonic-even. It is shown that the answer is positive if the isometric dimension of G equals its diameter which is in turn true for partial cubes with isometric dimension at most 6. Under an additional technical condition it is proved that an even partial cube G is harmonic-even or has two adjacent vertices whose diametrical verti...
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ژورنال
عنوان ژورنال: TvV Tijdschrift voor Verzorgenden
سال: 2018
ISSN: 0921-5832,2468-1350
DOI: 10.1007/s41183-018-0053-x