Oszthatatlanok

Oszthatatlanok is a term of Hungarian mathematics, referring to systems of objects in which certain subsets are forbidden from being split into two non-empty subsets, using the standard operation of dividing the objects in a set into two subsets. This concept is often used in combinatorial mathematics and theoretical computer science.

One of the key properties of oszthatatlanok is that they are often related to undirected graphs. An undirected graph is called an oszthatatlan graph if it is possible to assign integer weights to each of its vertices such that each edge's two endpoints sum to an integer, while not being able to partition all vertices into two non-empty disjoint sets whose edges' sums add up to the same integer.

Oszthatatlan graphs are connected graphs which are not forests and have a characteristic property that makes their edges non-decomposing. Mathematically, a graph is oszthatatlan if and only if for every edge, contracting it would make the resulting graph either connected and non-forest, or oscillating. Once a cycle is detected in a connected oszhatatlan graph, it is required to be optimized.

In the study of oszthatatlanok, various special types of graphs are often considered. An example is the series-parallel graph, which is an oszthatatlan graph that does not contain any cycles, and its set of edges can be decomposed into a series of disjoint cycles.

The study of oszthatatlanok involves solving problems related to connected graphs with an emphasis on non-decomposing and cyclic properties. Computer science has solutions to create different oszthatatlan graphs by making adjustments to regular graphs.