A proof of a sumset conjecture of Erdős

Each path of F √ n, √ n starts at the root, goes through some number of dashed trapezoids, having one vertex in each of them, reaches a suitable level, and then it turns into one of

In this paper, we study Ramsey numbers of graphs in Gallai colorings, where a Gallai coloring is a coloring of the edges of a complete graph without rainbow triangles (that is,

We give a combinatorial proof of the rank-unimodality of the poset of order ideals of a product of chains of lengths 2, n, and m, and find a symmetric chain decomposition in the

Unless stated otherwise, we shall use small letters such as x to denote positive inte- gers or functions or elements of a set, capital letters such as X to denote sets, and

Sauer and Spencer in their work [5] conjectured that if the minimum degree of G is at least 2n/3 then G contains every graph of order n with maximum degree of at most 2..

By restricting Fan’s condition to some induced subgraphs of 2- connected graphs, Ning and Zhang [9] extended Theorem 1 as follows.... This can be easily deduced from the

(4) Extension theorems are often used for optimal linear codes problem, especially to prove the nonexistence of linear codes with certain parameters.. Moreover, the extended matrix of

Corr´ adi and Hajnal [2] proved that if G is a graph of order at least 3k with minimum degree at least 2k, then G contains k independent cycles.. This result has inspired much