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In this paper, we first establish a coincidence theorem under the noncompact settings. Then we derive some fixed point theorems for a family of functions. We apply our fixed point theorem to study nonempty intersection problems for sets with convex sections and obtain a social equilibrium existence theorem. We also introduce a concept of a quasivariational(More)
We propose some 'local switching' search algorithms for finding large bipartite subgraphs in simple undirected graphs. The algorithms are based on the 'measure of effectiveness' of the bipartitions of the vertex set. We analyze the worst-case behavior of these algorithms, giving general lower bounds, and also prove that the concept of switching has its(More)
We formulate general boundary conditions for a labelling to assure the existence of a balanced n-simplex in a triangulated polyhedron. Furthermore we prove a Knaster-Kuratowski-Mazurkiewicz type theorem for polyhedrons and generalize some theorems of Ichiishi and Idzik. We also formulate a necessary condition for a continuous function defined on a(More)
A solid combinatorial theory is presented. The generalized Sperner lemma for chains is derived from the combinatorial Stokes formula. Many other generalizations follow from applications of an n-index of a labelling defined on chains with values in primoids. Primoids appear as the most general structure for which Sperner type theorems can be formulated.(More)
  • Adam Idzik
  • Discussiones Mathematicae Graph Theory
  • 2005
All graphs considered here are finite simple graphs, i.e., graphs without loops, multiple edges or directed edges. For a graph G = (V, E), where V is a vertex set and E is an edge set, we write sometimes V (G) for V and E(G) for E to avoid ambiguity. We shall write G \ v instead of G V \{v} = (V \ {v}, E ∩ 2 V \{v}), the subgraph induced by V \ {v}. A(More)