Ajai Kapoor

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Balanced 0, ±1 Matrices Part I. Decomposition

A 0, ±1 matrix is balanced if, in every square submatrix with two nonzero entries per row and col... more A 0, ±1 matrix is balanced if, in every square submatrix with two nonzero entries per row and column, the sum of the entries is a multiple of four. This paper extends the decomposition of balanced 0, 1 matrices obtained by Conforti, Cornuéjols, and Rao (1999, J. Combin. Theory Ser. B77, 292–406) to the class of balanced 0, ±1 matrices. As a consequence, we obtain a polynomial time algorithm for recognizing balanced 0, ±1 matrices.

Balanced 0, + or - Matrices. Part 2. Recognition Algorithm

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Balanced Matrices

A Theorem of Truemper

An important theorem due to Truemper characterizes the graphs whose edges can be labelled so that... more An important theorem due to Truemper characterizes the graphs whose edges can be labelled so that all chordless cycles have prescribed parities. This theorem has since proved an essential tool in the study of balanced matrices, graphs with no even length chordless cycle and graphs with no odd length chordless cycle of length greater than 3. In this paper we prove this theorem in a novel and elementary way and we derive some of its consequences. In particular, we show how to obtain Tutte&apos;s characterization of regular matrices.

Post Facto Identification and Prioritization of Causes of Buffer Consumption

Full-kit management in projects: determining the full-kit date

Recognizing Balanced 0, +/- Matrices

ABSTRACT

Finding an even hole in a graph

Proceedings 38th Annual Symposium on Foundations of Computer Science

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Facilitation of multi-project management using task hierarchy

A mickey-mouse decomposition theorem

Lecture Notes in Computer Science, 1995

A graph is signable to be without odd holes if we can assign labels “even” or “odd” to its edges ... more A graph is signable to be without odd holes if we can assign labels “even” or “odd” to its edges in such a way that the number of edges labelled “odd” in every triangle is odd and the number of edges labelled “odd” in every chordless cycle of length greater than three is even. Note that a graph has no odd holes if it is signed to be without odd holes with every edge having an “odd” label. We derive a co-NP characterization of such graphs.

Even and odd holes in cap‐free graphs

Journal of Graph Theory, 1999

It is an old problem in graph theory to test whether a graph contains a chordless cycle of length... more It is an old problem in graph theory to test whether a graph contains a chordless cycle of length greater than three (hole) with a specific parity (even, odd). Studying the structure of graphs without odd holes has obvious implications for Berge's strong perfect graph conjecture that states that a graph G is perfect if and only if neither G nor its complement contain an odd hole. Markossian, Gasparian, and Reed have proven that if neither G nor its complement contain an even hole, then G is β-perfect. In this article, we extend the problem of testing whether G(V, E) contains a hole of a given parity to the case where each edge of G has a label odd or even. A subset of E is odd (resp. even) if it contains an odd (resp. even) number of odd edges. Graphs for which there exists a signing (i.e., a partition of E into odd and even edges) that makes every triangle odd and every hole even are called even-signable. Graphs that can be signed so that every triangle is odd and every hole is odd are called odd-signable. We derive from a theorem due to Truemper co-NP characterizations of even-signable and odd-

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Balanced 0, ±1 Matrices I. Decomposition

Journal of Combinatorial Theory, Series B, 2001

A 0, \1 matrix is balanced if, in every square submatrix with two nonzero entries per row and col... more A 0, \1 matrix is balanced if, in every square submatrix with two nonzero entries per row and column, the sum of the entries is a multiple of four. This paper extends the decomposition of balanced 0, 1 matrices obtained by Conforti, Cornue jols, and Rao (1999, J. Combin. Theory Ser. B 77, 292 406) to the class of balanced 0, \1 matrices. As a consequence, we obtain a polynomial time algorithm for recognizing balanced 0, \1 matrices.

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Perfect, ideal and balanced matrices

European Journal of Operational Research, 2001

In this paper, we survey results and open problems on perfect, ideal and balanced matrices. These... more In this paper, we survey results and open problems on perfect, ideal and balanced matrices. These matrices arise in connection with the set packing and set covering problems, two integer programming models with a wide range of applications. We concentrate on some of the beautiful polyhedral results that have been obtained in this area in the last thirty years. This survey rst appeared in Ricerca Operativa.

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A Theorem of Truemper

Combinatorica, 2000

An important theorem due to Truemper characterizes the graphs whose edges can be labeled so that ... more An important theorem due to Truemper characterizes the graphs whose edges can be labeled so that all chordless cycles have prescribed parities. This theorem has proven to be an essential tool in the study of various objects like balanced matrices, graphs with no even length chordless cycle and graphs with no odd length chordless cycle with at least five edges. In this paper we prove this theorem in a novel and elementary way and derive some of its consequences. In particular, we show an easy way to obtain Tutte's characterization of regular matrices.

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Perfect matchings in balanced hypergraphs

Combinatorica, 1996

... 0209 9683/96/$6.00 @1996 Akad6miai Kiad6, Budapest Page 2. 326 M. CONFORTI, O. CORNUISJOLS, A... more

Universally signable graphs

Combinatorica, 1997

In a graph, a chordless cycle of length greater than three is called a hole. Let be a f0; 1g vect... more In a graph, a chordless cycle of length greater than three is called a hole. Let be a f0; 1g vector whose entries are in one-to-one correspondence with the holes of a graph G. We characterize graphs for which, for all choices of the vector , we can pick a subset F of the edge set of G such that jF \ Hj H (mod 2), for all holes H of G and jF \ T j 1 for all triangles T of G. We call these graphs universally signable. The subset F of edges is said to be labelled odd. All other edges are said to be labelled even. Clearly graphs with no holes (triangulated graphs) are universally signable with a labelling of odd on all edges, for all choices of the vector . We give a decomposition theorem which leads to a good characterization of graphs that are universally signable. This is a generalization of a theorem due to Hajnal and Suranyi 3] for triangulated graphs.

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Balanced 0, ±1 Matrices II. Recognition Algorithm

Journal of Combinatorial Theory, Series B, 2001

In this paper we give a polynomial time recognition algorithm for balanced 0, \1 matrices. This a... more

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Ajai Kapoor

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