Combinatorial characterization of read-once formulae
Discrete Mathematics - Special issue on combinatorics and algorithms
Journal of Graph Theory
Imperfect and Nonideal Clutters: A Common Approach
Combinatorica
Proof of Chv&tal's conjecture on maximal stable sets and maximal cliques in graphs
Journal of Combinatorial Theory Series B
Corrigendum to proof of Chvátal's conjecture on maximal stable sets and maximal cliques in graphs
Journal of Combinatorial Theory Series B
Edge colorings of complete graphs without tricolored triangles
Journal of Graph Theory
An improvement on the complexity of factoring read-once Boolean functions
Discrete Applied Mathematics
Colored graphs without colorful cycles
Combinatorica
Decomposing complete edge-chromatic graphs and hypergraphs. Revisited
Discrete Applied Mathematics
A Characterization of Almost CIS Graphs
SIAM Journal on Discrete Mathematics
Characterizing (quasi-)ultrametric finite spaces in terms of (directed) graphs
Discrete Applied Mathematics
| Hi-index | 0.04 |
Let us consider two binary systems of inequalities (i) Cx=e and (ii) Cx@?e, where C@?{0,1}^m^x^n is an mxn(0,1)-matrix, x@?{0,1}^n, and e is the vector of m ones. The set of all support-minimal (respectively, support-maximal) solutions x to (i) (respectively, to (ii)) is called the blocker (respectively, anti-blocker). A blocker B (respectively, anti-blocker A) is called exact if Cx=e for every x@?B (respectively, x@?A). Exact blockers can be completely characterized. There is a one-to-one correspondence between them and P"4-free graphs (along with a well-known one-to-one correspondence between the latter and the so-called read-once Boolean functions). However, the class of exact anti-blockers is wider and more sophisticated. We demonstrate that it is closely related to the so-called CIS graphs, more general @?-CIS d-graphs, and @D-conjecture.