In this paper we study restrictions imposed on individual preferences, as opposed to preference profiles, and we introduce individual preference restrictions that characterize the existence and uniqueness of stable hedonic coalition structures on rich preference domains. We prove that if such a preference domain satisfies an individual preference restriction then it guarantees the existence of ...

We prove a sufficient condition for a graph G to have a matching that interconnects all the components of a disconnected spanning subgraph ofG. The condition is derived from a recent extension of the Matroid intersection theorem due to Aharoni and Berger. We apply the result to the problem of the existence of a (spanning) 2-walk in sufficiently tough graphs.

Assume that G = G(V, E) is an undirected graph with vertex set V and edge set E. A clique of G is a complete subgraph. An edge clique-covering is a family of cliques of G which cover all edges of G. The edge clique-cover number, Be( G), is the minimum number of cliques in an edge clique-cover of G. For results and applications of the edge clique-cover number see [1-4]. Observe that Be(G) does n...

Given a combinatorial designD with block set B, its traditional block-intersection graph GD is the graph having vertex set B such that two vertices b1 and b2 are adjacent if and only if b1 and b2 have non-empty intersection. In this paper we consider the S-block-intersection graph, in which two vertices b1 and b2 are adjacent if and only if |b1 ∩ b2| ∈ S. As our main result we prove that {1, 2,...

The notions of relaxed submonotone and relaxed monotone mappings in Banach spaces are introduced and many of their properties are investigated. For example, the Clarke subdifferential of a locally Lipschitz function in a separable Banach space is relaxed submonotone on a residual subset. For example, it is shown that this property need not be valid on the whole space. We prove, under certain hy...

Abstract: The intersection dimension of a graph G with respect to a class A of graphs is the minimum k such that G is the intersection of some k graphs on the vertex set V (G) belonging to A. In this paper we follow [ Kratochv́ıl J., Tuza Z.: Intersection dimensions of graph classes, Graphs and Combinatorics 10 (1994), 159– 168 ] and show that for some pairs of graph classes A, B the intersectio...

We introduce the (general) homotopy groups of spheres as link invariants for Brunnian-type links through the investigations on the intersection subgroup of the normal closures of the meridians of strongly nonsplittable links. The homotopy groups measure the difference between the intersection subgroup and symmetric commutator subgroup of the normal closures of the meridians and give the invaria...

In this article we consider the intersection graph G(R) of nontrivial proper ideals of a finite commutative principal ideal ring R with unity 1. Two distinct ideals are adjacent if they have non-trivial intersection. We characterize when the intersection graph is complete, bipartite, planar, Eulerian or Hamiltonian. We also find a formula to calculate the number of ideals in each ring and the d...

The co-maximal subgroup graph $$\Gamma (G)$$ of a group G is whose vertices are non-trivial proper subgroups and two H K adjacent if $$HK=G$$ . In this paper, we continue the study , especially when has isolated vertices. We define new ^*(G)$$ which obtained by removing from characterize connected, complete graph, star an universal vertex etc. also find various parameters like diameter, girth, ...

‎Let $G$ be a finite group which is not a cyclic $p$-group‎, ‎$p$ a prime number‎. ‎We define an undirected simple graph $Delta(G)$ whose‎ ‎vertices are the proper subgroups of $G$, which are not contained in the‎ ‎Frattini subgroup of $G$ and two vertices $H$ and $K$ are joined by an edge‎ ‎if and only if $G=langle H‎ , ‎Krangle$‎. ‎In this paper we classify finite groups with planar graph‎. ‎...