The Satisfactory Partition problem asks for deciding if a given graph has a partition of its
vertex set into two nonempty parts such that each vertex has at least as many neighbors in …

Degree Conditions for the Existence of Vertex-Disjoint Cycles and Paths: A Survey |
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Any reasonably large group of individuals, families, states, and parties exhibits the
phenomenon of subgroup formations within the group such that the members of each group …

In a given graph, we want to partition the set of its vertices into two subsets, such that each
vertex is satisfied in that it has at least as many neighbours in its own subset as in the other …

Understanding how the cycles of a graph or digraph behave in general has always been an
important point of graph theory. In this paper, we study the question of finding a set of $ k …

A celebrated theorem of Stiebitz 13 asserts that any graph with minimum degree at least can
be partitioned into two parts that induce two subgraphs with minimum degree at least s and t …

Stiebitz [Decomposing graphs under degree constraints, J. Graph Theory 23 (1996) 321–
324] proved that if every vertex v in a graph G has degree d (v)⩾ a (v)+ b (v)+ 1 (where a and …

Graph partitioning problem, which is one of the most important topics in graph theory,
usually asks for a partition of the vertex set of a graph into pairwise disjoint subsets with …

Let s, t be two integers, and let g (s, t) denote the minimum integer such that the vertex set of
a graph of minimum degree at least g (s, t) can be partitioned into two nonempty sets which …

Abstract The Erdős–Lovász Tihany conjecture asserts that every graph G with) contains two
vertex disjoint subgraphs G1 and G2 such that and. Under the same assumption on G, we …