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- Qamrul Hasan Ansari, Adam Idzik, Jen-Chih Yao, Juliusz P. Schauder
- 2000

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)

- Stanislaw Bylka, Adam Idzik, Jan Komar
- Graphs and Combinatorics
- 1999

- Stanislaw Bylka, Adam Idzik, Zsolt Tuza
- Discrete Mathematics
- 1999

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)

- NONORIENTED PSEUDOMANIFOLDS, Adam Idzik, Konstanty Junosza-Szaniawski, Konstanty Junosza-Szaniawski
- 2007

Sperner lemma type theorems are proved for nonoriented primoids and pseudomanifolds. A rank function of a primoid is defined. Applications of these theorems to the geometric simplex are given. Also Knaster– Kuratowski–Mazurkiewicz type theorems on covering of the geometric simplex are presented.

- Adam Idzik, Gyula O. H. Katona, Rajiv Vohra
- J. Comb. Theory, Ser. A
- 2001

Suppose that any t members (t ≥ 2) of a regular family on an n element set have at least k common elements. It is proved that the largest member of the family has at least k1/tn1−1/t elements. The same holds for balanced families, which is a generalization of the regularity. The estimate is asymptotically sharp.

- Adam Idzik, Zsolt Tuza
- Discrete Mathematics
- 2001

- Adam Idzik, Konstanty Junosza-Szaniawski
- Discussiones Mathematicae Graph Theory
- 2005

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)

- Adam Idzik, Marek Izydorek, Juliusz P. Schauder
- 2008

A generalization of the theorem of Zhong on the product of spheres to multivalued maps is given. We prove also a stronger result of Bourgin–Yang type.

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)