Discrete Mathematics Research Papers - Academia.edu (original) (raw)
Two general methods for establishing the logarithmic behavior of recursively defined sequences of real numbers are presented. One is the interlacing method, and the other one is based on calculus. Both methods are used to prove... more
Two general methods for establishing the logarithmic behavior of recursively defined sequences of real numbers are presented. One is the interlacing method, and the other one is based on calculus. Both methods are used to prove logarithmic behavior of some combinatorially relevant sequences, such as Motzkin and Schr\"oder numbers, sequences of values of some classic orthogonal polynomials, and many others. The calculus method extends also to two- (or more-) indexed sequences.
A graph GGG with a list of colors L(v)L(v)L(v) and weight w(v)w(v)w(v) for each vertex vvv is (L,w)(L,w)(L,w)-colorable if one can choose a subset of w(v)w(v)w(v) colors from L(v)L(v)L(v) for each vertex vvv, such that adjacent vertices receive disjoint color sets. In... more
A graph GGG with a list of colors L(v)L(v)L(v) and weight w(v)w(v)w(v) for each vertex vvv is (L,w)(L,w)(L,w)-colorable if one can choose a subset of w(v)w(v)w(v) colors from L(v)L(v)L(v) for each vertex vvv, such that adjacent vertices receive disjoint color sets. In this paper, we give necessary and sufficient conditions for a weighted path to be (L,w)(L,w)(L,w)-colorable for some list assignments LLL. Furthermore, we solve the problem of the free-choosability of a cycle.
A graph is well-covered if every maximal independent set has the same cardinality. The recognition problem of well-covered graphs is known to be co-NP-complete. Let w be a weight function defined on the vertices of G. Then G is... more
A graph is well-covered if every maximal independent set has the same cardinality. The recognition problem of well-covered graphs is known to be co-NP-complete. Let w be a weight function defined on the vertices of G. Then G is w-well-covered if all maximal independent sets of G are of the same weight. The set of weight functions w for which a graph is w-well-covered is a vector space. We prove that finding the vector space of weight functions under which an input graph is w-well-covered can be done in polynomial time, if the input graph does not contain cycles of length 4, 5, 6 and 7.
We give short elementary expositions of combinatorial proofs of some variants of Euler's partitition problem that were first addressed analytically by George Andrews, and later combinatorially by others. Our methods, based on ideas... more
We give short elementary expositions of combinatorial proofs of some variants of Euler's partitition problem that were first addressed analytically by George Andrews, and later combinatorially by others. Our methods, based on ideas from a previous paper by the author , enable us to state and prove new generalizations of two of these results.
A dynamic thermal-hydraulic mathematical model of the evaporator dynamics of a once - through sub critical steam generator was derived and presented. This model allows the investigation of evaporator dynamics including its transient... more
A dynamic thermal-hydraulic mathematical model of the evaporator dynamics of a once - through sub critical steam generator was derived and presented. This model allows the investigation of evaporator dynamics including its transient responses. The evaporator was considered as part of a three-section (economizer, evaporator and super-heater) model with time varying phase boundaries and was described by a set of linearized discrete - difference equations which, with some other algebraic equations, constituted a closed system of equations possible for exact computer solution. This model was derived using the fundamental equations of mass, energy and momentum balance. For the first time, a discrete differential approach was applied in order to investigate such complex, two phase processes. Namely, this approach allows one to escape from the model of this process usually described by a set of partial differential equations and enables one, using this method, to simulate evaporator dynami...
A straight-ahead walk in an embedded Eulerian graph G always passes from an edge to the opposite edge in the rotation at the same vertex. A straight-ahead walk is called Eulerian if all the edges of the embedded graph G are traversed in... more
A straight-ahead walk in an embedded Eulerian graph G always passes from an edge to the opposite edge in the rotation at the same vertex. A straight-ahead walk is called Eulerian if all the edges of the embedded graph G are traversed in this way starting from an arbitrary edge. An embedding that contains an Eulerian straight-ahead walk is called an Eulerian embedding. In this article, we characterize some properties of Eulerian embeddings of graphs and of embeddings of graphs such that the corresponding medial graph is Eulerian embedded. We prove that in the case of 4-valent planar graphs, the number of straight-ahead walks does not depend on the actual embedding in the plane. Finally, we show that the minimal genus over Eulerian embeddings of a graph can be quite close to the minimal genus over all embeddings.
For an edge-weighted connected undirected graph, the minimum k-way cut problem is to find a subset of edges of minimum total weight whose removal separates the graph into k connected components. The problem is NP-hard when k is part of... more
For an edge-weighted connected undirected graph, the minimum k-way cut problem is to find a subset of edges of minimum total weight whose removal separates the graph into k connected components. The problem is NP-hard when k is part of the input and W[1]-hard when k is taken as a parameter. A simple algorithm for approximating a minimum k-way cut
discrete math - recurrence relation example
The map which takes a square matrix to its tropical eigenvalue-eigenvector pair is piecewise linear. We determine the cones of linearity of this map. They are simplicial but they do not form a fan. Motivated by statistical ranking, we... more
The map which takes a square matrix to its tropical eigenvalue-eigenvector pair is piecewise linear. We determine the cones of linearity of this map. They are simplicial but they do not form a fan. Motivated by statistical ranking, we also study the restriction of that cone decomposition to the subspace of skew-symmetric matrices.
System specifications are a series of statements that spell out the requirements of the system in question. The specifications are said to be consistent if there is an assignment of truth values to the variables in the expressions that... more
System specifications are a series of statements that spell out the requirements of the system in question. The specifications are said to be consistent if there is an assignment of truth values to the variables in the expressions that makes all the expressions true.
Sana UllahΨ , Murad Ali+, Md. Asdaque HussainΨ, and Kyung Sup KwakΨ Ψ Graduate School of IT and Telecommunications, Inha University 253 Yonghyun-Dong, Nam-Gu, Incheon 402-751, South Korea. + KDI School of Public Policy and Management 87... more
Sana UllahΨ , Murad Ali+, Md. Asdaque HussainΨ, and Kyung Sup KwakΨ Ψ Graduate School of IT and Telecommunications, Inha University 253 Yonghyun-Dong, Nam-Gu, Incheon 402-751, South Korea. + KDI School of Public Policy and Management 87 Hoegiro ...