A5041495224- Advanced Graph Theory Research
- Limits and Structures in Graph Theory
- Graph Labeling and Dimension Problems
- Graph theory and applications
- Computational Geometry and Mesh Generation
- graph theory and CDMA systems
- Interconnection Networks and Systems
- Optimization and Search Problems
- Complexity and Algorithms in Graphs
- Finite Group Theory Research
- Metal-Organic Frameworks: Synthesis and Applications
- Coding theory and cryptography
- Advanced Research in Systems and Signal Processing
- Structural Analysis and Optimization
- Mathematical Dynamics and Fractals
- Geometric and Algebraic Topology
- Advanced Banach Space Theory
- Multi-Agent Systems and Negotiation
- Photochromic and Fluorescence Chemistry
- Advanced Topology and Set Theory
- Point processes and geometric inequalities
- Genome Rearrangement Algorithms
- Synthesis of Indole Derivatives
- Power Line Communications and Noise
- semigroups and automata theory
Technische Universität Ilmenau
2011-2023
Masaryk University
2021
University of Pavol Jozef Šafárik
2019
For a graph G on vertex set V = {1, …, n } let k ( 1 , ) be an integral vector such that [les ] i d for ∈ where is the degree of in . A -dominating D ⊆ every [setmn has at least neighbours The -domination number γ cardinality smallest · 1, corresponds to usual concept domination. Our approach yields improvement upper bound domination found by N. Alon and J. H. Spencer. If then notion complement independent set. function f p defined, it will proved min ), minimum taken over -dimensional cube...
In a graph G, vertex dominates itself and its neighbors. A subset S µ V (G) is double dominating set of G if every at least twice. The minimum cardinality the domination number ∞£2(G). function f(p) deflned, it shown that ∞£2(G) = minf(p), where taken over n-dimensional cube C n fp (p1;:::;pn) j pi 2 IR;0 • 1;i 1;:::;ng. Using this result, then has order with degree ‐ average d, ((ln(1 + d) ln‐ 1)=‐)n.
Abstract The well‐known lower bound on the independence number of a graph due to Caro (Technical Report, Tel‐Aviv University, 1979) and Wei Memorandum, TM 81 ‐ 11217 9, Bell Laboratories, 1981) can be established as performance guarantee two natural simple greedy algorithms or randomized algorithm. We study possible generalizations improvements these approaches using vertex weights discuss conditions so‐called potential functions p G : V ( )→ℕ 0 defined set for which suitably modified...
Let F be a set of graphs and for graph G let F(G) (G) denote the maximum order an induced subgraph which does not contain in as subgraph, respectively. Lower bounds on are presented.
Abstract Menger's Theorem for digraphs states that any two vertex sets A and B of a digraph D such cannot be separated from by set at most t vertices, there are + 1 disjoint – ‐paths in . Here short elementary proof more general theorem is given. © 2001 John Wiley & Sons, Inc. J Graph Theory 37: 35–36,
For a finite undirected graph G on n vertices some continuous optimization problems taken over the n-dimensional cube are presented and it is proved that their optimum values equal independence number of G.
For a connected and non-complete graph, new lower bound on its independence number is proved.It shown that this realizable by the well known efficient algorithm MIN.
For a simple planar graph G and positive integer k, we prove the upper bound 2(n − 1)k + 4k(n 4) 2·3k 2((δ δk)(3n 6 m) on sum of kth powers degrees G, where n, m, δ are order, size, minimum degree respectively. The is tight for all m with 0⩽3n m≤⌊n/2⌋ 2 = 3. We also present bounds in terms degree, maximum G. © 2010 Wiley Periodicals, Inc. J Graph Theory 67:112-123, 2011