Balancing Connected Colourings of Graphs
نویسندگان
چکیده
We show that the edges of any graph $G$ containing two edge-disjoint spanning trees can be blue/red coloured so blue and red graphs are connected degrees at each vertex differ by most four. This improves a result H\"orsch. discuss variations question for digraphs, infinite computational question, resolve further questions H\"orsch in negative.
منابع مشابه
Colourings in Bipartite Graphs
The concept of X-chromatic partition and hyper independent chromatic partition of bipartite graphs were introduced by Stephen Hedetniemi and Renu Laskar. We find the bounds for X-chromatic number and hyper independent chromatic number of a bipartite graph. The existence of bipartite graph with χh(G)=a and γY(G)=b-1, χh(G)=a and χX(G)=b where a ≤b are proved. We also prove the existence of bipar...
متن کاملClique Colourings of Geometric Graphs
A clique colouring of a graph is a colouring of the vertices such that no maximal clique is monochromatic (ignoring isolated vertices). The least number of colours in such a colouring is the clique chromatic number. Given n points x1, . . . ,xn in the plane, and a threshold r > 0, the corresponding geometric graph has vertex set {v1, . . . , vn}, and distinct vi and vj are adjacent when the Euc...
متن کاملDelay Colourings of Cubic Graphs
In this note we prove the conjecture of Wilfong, Haxell and Winkler (2001) that every bipartite multigraph with integer edge delays admits an edge colouring with d + 1 colours in the special case where d = 3. A connection to the Brualdi-RyserStein conjecture is discussed.
متن کاملList colourings of planar graphs
Let G = (V,E) be a graph, let f : V (G)→ N, and let k ≥ 0 be an integer. A list-assignment L of G is a function that assigns to each vertex v of G a set (list) L(v) of colors: usually each color is a positive integer. We say that L is an f -assignment if |L(v)| = f(v) for all v ∈ V , and a k-assignment if |L(v)| = k for all v ∈ V . A coloring ofG is a function φ that assigns a color to each ver...
متن کاملDistance-regular graphs, MH-colourings and MLD-colourings
It is shown that the only bipartite distance regular graphs of diameter 3 which are MLDcolourable are the incidence graphs of complementary Hadamard designs.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Electronic Journal of Combinatorics
سال: 2023
ISSN: ['1077-8926', '1097-1440']
DOI: https://doi.org/10.37236/11256