… x1,...,xk as a rooted minor, where the edge set of H is defined in … would like to obtain as a
minor. This graph should capture the … if and only if they belong to the same Kempe chain in G. …

A transversal of a partition is a set which contains exactly one member from each member of
the partition and nothing else. We study the following problem. Given a transversal T of a …

… Motivated by Theorems 2.21 and 2.26, Kriesell postulated the following conjecture about
rooted minors in graphs admitting a Kempe colouring, which serves as opening question for …

Escaping Nazi Germany, young Henry Kempe immigrated to the United States, and became
a pediatrician and virologist specializing in smallpox. But ever the medical maverick, he …

… Kempe chains, the condition that afflicted Kempe’s attempted proof of the 4-color theorem
(see [2]). If an i-j Kempe chain and a j-k Kempe chain, i ≠ k … With only minor modifications, this …

… Because each P i is a Kempe chain, by Lemma 1.9 the subgraph of G induced by V ( P 1 )
∪ V ( P 2 ) ∪ V ( P 5 ) ∪ V ( P 6 ) contains a K 4 minor rooted at { y 1 , y 2 , z 1 , z 2 } . With this …

… ensure that G contains H as a rooted minor or minor. This naturally leads to studying sets of
… a Kempe chain connecting u and v.1 Remark 3.2.6 ensures that these Kempe chains contain …

… minors obtained in this paper, generalized Kempe chains of contraction-critical graphs by
Rolek and the second author, and the method for finding K7 minors … a K4 minor rooted at z1,z2,…

… “Kempe-chain” H, an absolutely classic process in graph coloring theory. The term Kempe-…
Only little progress has been made so far on generalizing Theorem 5 to “rooted K 5 -minors”…

… We are also given a root node r, a set P C_ V \ {r} of positive nodes, and a disjoint set N C_
… edge with a chain of degree-2 vertices. We say that G contains H as a topological minor if it …