2-3 graphs which have Vizing's adjacency property.
2-distance 4-colorability of planar subcubic graphs with girth at least 22
The trivial lower bound for the 2-distance chromatic number χ₂(G) of any graph G with maximum degree Δ is Δ+1. It is known that χ₂ = Δ+1 if the girth g of G is at least 7 and Δ is large enough. There are graphs with arbitrarily large Δ and g ≤ 6 having χ₂(G) ≥ Δ+2. We prove the 2-distance 4-colorability of planar subcubic graphs with g ≥ 22.
2-distance coloring of sparse planar graphs.
2-Tone Colorings in Graph Products
A variation of graph coloring known as a t-tone k-coloring assigns a set of t colors to each vertex of a graph from the set {1, . . . , k}, where the sets of colors assigned to any two vertices distance d apart share fewer than d colors in common. The minimum integer k such that a graph G has a t- tone k-coloring is known as the t-tone chromatic number. We study the 2-tone chromatic number in three different graph products. In particular, given graphs G and H, we bound the 2-tone chromatic number...
3-consecutive c-colorings of graphs
A 3-consecutive C-coloring of a graph G = (V,E) is a mapping φ:V → ℕ such that every path on three vertices has at most two colors. We prove general estimates on the maximum number of colors in a 3-consecutive C-coloring of G, and characterize the structure of connected graphs with for k = 3 and k = 4.
4-critical 4-valent planar graphs constructed with crowns.
𝓟-bipartitions of minor hereditary properties
We prove that for any two minor hereditary properties 𝓟₁ and 𝓟₂, such that 𝓟₂ covers 𝓟₁, and for any graph G ∈ 𝓟₂ there is a 𝓟₁-bipartition of G. Some remarks on minimal reducible bounds are also included.
γ-Cycles And Transitivity By Monochromatic Paths In Arc-Coloured Digraphs
We call the digraph D an m-coloured digraph if its arcs are coloured with m colours. If D is an m-coloured digraph and a ∈ A(D), colour(a) will denote the colour has been used on a. A path (or a cycle) is called monochromatic if all of its arcs are coloured alike. A γ-cycle in D is a sequence of vertices, say γ = (u0, u1, . . . , un), such that ui ≠ uj if i ≠ j and for every i ∈ 0, 1, . . . , n there is a uiui+1-monochromatic path in D and there is no ui+1ui-monochromatic path in D (the indices...
Ациклический хроматический класс графа
Графы сводимости и их построение для некоторых задач
Групповые раскраски полных двудольных графов и оценки чисел Хегквиста
Дистрибутивные группоиды в теории узлов
Метод трехцветного раскрашивания графов.
Некоторые свойства ребернокритических графов
Некоторые свойства слабоодносвязных гиперграфов и их приложения
О 3-хроматических плоских гиперграфах
О раскраске гиперграфов
О характеризации хроматически-жестких многочленов.
Об одной задаче окрашивания
Об одном комбинаторном неравенстве