Reconfiguration is concerned with relationships among solutions to a problem instance,
where the reconfiguration of one solution to another is a sequence of steps such that each …

Graph edge coloring has a rich theory, many applications and beautiful conjectures, and it is
studied not only by mathematicians, but also by computer scientists. In this survey, written for …

In graph theory, reconfiguration is concerned with relationships among solutions to a given
problem for a specific graph. The reconfiguration of one solution into another occurs via a …

Let G be a graph with a vertex colouring α. Let a and b be two colours. Then a connected
component of the subgraph induced by those vertices coloured either a or b is known as a …

业已证明四色猜想的数学证明可归结为刻画4-色漏斗型伪唯一4-色极大平面图的特征.
为刻画此类极大平面图的结构特征, 本文提出一种构造极大平面图的方法扩缩运算. 研究发现 …

设G 是一个k-色图, 若G 的所有k-着色是Kempe 等价的, 则称G 为Kempe 图. 表征色数3
的Kempe 图特征是一尚待解决难题. 该文对极大平面图的Kempe 等价性进行了研究 …

Given a graph G=(V, E) and a proper vertex colouring of G, a Kempe chain is a subset of V
that induces a maximal connected subgraph of G in which every vertex has one of two …

Kempe equivalence of 4-critical planar graphs arXiv:2101.04065v3 [math.CO] 4 Jul 2022
Page 1 Kempe equivalence of 4-critical planar graphs Carl Feghali ∗ Abstract Answering a …

Applications of graph colouring often involve taking restrictions into account, and it is
desirable to have multiple (disjoint) solutions. In the optimal case, where there is a partition …

Let G be a k-chromatic graph. G is called a Kempe graph if all k-colorings ofG are Kempe
equivalent. It is an unsolved and hard problem to characterize the properties of Kempe …