The list-chromatic index ofK6

The list - chromatic index of K 8 and K 10

In [4], Cariolaro et al. demonstrated how colorability problems can be approached numerically by the use of computer algebra systems and the Combinatorial Nullstellensatz. In particular, they verified a case of the List Coloring Conjecture by proving that the list-chromatic index of K6 is 5. In this short note, we show that using the coefficient formula of Schauz [16] is much more efficient tha...

On the list chromatic index of nearly bipartite multigraphs

Galvin ([7]) proved that every k-edge-colorable bipartite multigraph is kedge-choosable. Slivnik ([11]) gave a streamlined proof of Galvin's result. A multigraph G is said to be nearly bipartite if it contains a special vertex Vs such that G Vs is a bipartite multigraph. We use the technique in Slivnik's proof to obtain a list coloring analog of Vizing's theorem ([12]) for nearly bipartite mult...

The circular chromatic index

The list chromatic index of simple graphs whose odd cycles intersect in at most one edge

We study the class of simple graphs G for which every pair of distinct odd cycles intersect in at most one edge. We give a structural characterization of the graphs in G and prove that every G ∈ G satisfies the list-edge-coloring conjecture. When ∆(G) ≥ 4, we in fact prove a stronger result about kernel-perfect orientations in L(G) which implies that G is (m∆(G) : m)edge-choosable and ∆(G)-edge...

List Index

This theory provides functions for finding the index of an element in a list, by predicate and by value. theory List-Index imports Main begin This theory collects functions for index-based manipulation of lists. 0.1 Finding an index This subsection defines three functions for finding the index of items in a list: find-index P xs finds the index of the first element in xs that satisfies P. index...