This monograph is an outcome of the Oberwolfach Seminar on Positional Games, given by
the authors at the Mathematisches Forschungsinstitut Oberwolfach (MFO) in Oberwolfach …

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This paper proves that every planar graph G contains a matching M such that the Alon-Tarsi
number of G− M is at most 4. As a consequence, G− M is 4-paintable, and hence G itself is 1 …

We initiate the study of applying the Combinatorial Nullstellensatz to the DP-coloring of
graphs even though, as is well-known, the Alon–Tarsi theorem does not apply to DP …

This paper constructs a planar graph $ G_1 $ such that for any subgraph $ H $ of $ G_1 $
with maximum degree $\Delta (H)\le 3$, $ G_1-E (H) $ is not $3 $-choosable, and a planar …

We study the list chromatic number of Cartesian products of graphs through the Alon-Tarsi
number as defined by Jensen and Toft (1995) in their seminal book on graph coloring …

In this thesis we study list coloring which was introduced independently by Vizing and Erdos,
Rubin, and Taylor in the 1970's. Suppose we associate a list assignment L with a graph G …

The Alon-Tarsi number of a graph $ G $ is the smallest $ k $ for which there is an orientation
$ D $ of $ G $ with max outdegree $ k-1$ such that the number of Eulerian subgraphs of $ G …

We extend the concept of the Alon–Tarsi number for unsigned graph to signed one.
Moreover, we introduce the modulo Alon–Tarsi number for a prime number p. We show that …

Abstract A (p, 1)-total labelling of a graph G is a mapping f: V (G)∪ E (G)→{0, 1,⋯, k} such
that| f (u)-f (v)|≥ 1 if uv∈ E (G),| f (e 1)-f (e 2)|≥ 1 if e 1 and e 2 are two adjacent edges in G …