Combinatorial Nullstellensatz is a novel theorem in algebra introduced by Noga Alon to
tackle combinatorial problems in diverse areas of mathematics. This book focuses on the …

Abstract A (d, h)-decomposition of a graph G is an ordered pair (D, H) such that H is a
subgraph of G of maximum degree at most h and D is an acyclic orientation of G− E (H) with …

The Alon–Tarsi number of planar graphs without cycles of lengths 4 and l - ScienceDirect
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Given a graph G with a set F (v) of forbidden values at each v∈ V (G), an F-avoiding
orientation of G is an orientation in which deg+(v)∉ F (v) for each vertex v. Akbari …

Given a graph GG, a decomposition of GG is a partition of its edges. A graph is (d, h) (d,h)‐
decomposable if its edge set can be partitioned into ad d‐degenerate graph and a graph …

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 …

A graph G has a (d, h)-decomposition if there is a pair (D, F) such that F is a subgraph of G
and D is an acyclic orientation of G− E (F), where the maximum degree of F is no more than …

Let Γ be an Abelian group and let G be a simple graph. We say that G is Γ-colorable if for
some fixed orientation of G and every edge labeling ℓ: E (G)→ Γ, there exists a vertex …

For a graph $ G $, by $\chi_2 (G) $ we denote the minimum integer $ k $, such that there is a
$ k $-coloring of the vertices of $ G $ in which vertices at distance at most 2 receive distinct …

Bernshteyn and Lee defined a new notion, weak degeneracy, which is slightly weaker than
the ordinary degeneracy. It is proved that strictly $ f $-degenerate transversal is a common …