In the paper the authors combine two so far separated areas of additive number theory. The first one builds on generalizations of Erdös-Ginzbur-Ziv theorem, while the second one on the fundamental Kneser’s theorem. Their main theorem turns out to imply several results that were so far unrelated. Although this paper presents a climax of certain field, the results imply possibility of further generalizations, going to the direction of the far-reaching Seymour-Schrijver hypothesis that combines the algebraic and the combinatorial side of additive number theory through the matroid theory.
COBISS.SI-ID: 15116377
In the paper a new approach is presented of the so-called fair reception, using which we have generalized the well-known 30 years old result of Barcalkin and German, and in this way established so far the largest known family of graphs that satisfy Vizing’s conjecture. Along the way, using the new concept, we derived an alternative proof of the result of Aharoni, Berger and Ziv, stating that the chordal graphs satisfy Vizing’s conjecture.
COBISS.SI-ID: 15170393