The problem of error-free transmission capacity of a noisy channel was posed by Shannon
in 1956 and remains unsolved, Nevertheless, partial results for this and similar channel and …

We show some consequences of results of Gallai concerning edge colorings of complete
graphs that contain no tricolored triangles. We prove two conjectures of Bialostocki and …

A Gallai‐coloring of a complete graph is an edge coloring such that no triangle is colored
with three distinct colors. Gallai‐colorings occur in various contexts such as the theory of …

We examine the combinatorial or probabilistic definition (“Boltzmann's principle”) of the
entropy or cross-entropy function H∝ \rmlnW or D∝-\rmlnP, where W is the statistical weight …

We prove that every 3-coloring of the edges of the complete graph on n vertices without a
rainbow triangle contains a set of order Ω (n 1/3 log 2⁡ n) which uses at most two colors …

An edge coloring of a graph G is a Gallai coloring if it contains no rainbow triangle. We show
that the number of Gallai r-colorings of K_n is (r2+o(1))2^n2. This result indicates that almost …

An edge coloring of the n-vertex complete graph, K n, is a Gallai coloring if it does not
contain any rainbow triangle, that is, a triangle whose edges are colored with three distinct …

Abstract Let G:=(G 1, G 2, G 3) be a triple of graphs on the same vertex set V of size n. A
rainbow triangle in G is a triple of edges (e 1, e 2, e 3) with ei∈ G i for each i and {e 1, e 2, e …

We study Ramsey-type problems in Gallai-colorings. Given a graph H and an integer k≥ 1,
the Gallai–Ramsey number GR k (H) is the least positive integer n such that every k-coloring …

Gallai-colorings of complete graphs–edge colorings such that no triangle is colored with
three distinct colors–occur in various contexts such as the theory of partially ordered sets (in …