# Alexandr V. Kostochka

- Publications
- Influence

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**public sources and our publisher partners.**The aim of this paper is to show that the minimum Hadwiger number of graphs with average degreek isO(k/√logk). Specially, it follows that Hadwiger’s conjecture is true for almost all graphs withn… Expand

This paper exploits the remarkable new method of Galvin (J. Combin. Theory Ser. B63(1995), 153?158), who proved that the list edge chromatic number??list(G) of a bipartite multigraphGequals its edge… Expand

Grunbaum's conjecture on the existence of k-chromatic graphs of degree k and girth g for every k ≥ 3, g ≥ 3 is disproved. In particular, the bound obtained states that the chromatic number of a… Expand

The independence numberαH of a hypergraph H is the size of a largest set of vertices containing no edge of H. In this paper, we prove that if Hn is an n-vertex r+1-uniform hypergraph in which every… Expand

A graph G is k-critical if it has chromatic number k, but every proper subgraph of G is ( k - 1 ) -colorable. Let f k ( n ) denote the minimum number of edges in an n-vertex k-critical graph. We give… Expand

Abstract This paper starts with a discussion of several old and new conjectures about choosability in graphs. In particular, the list-colouring conjecture, that ch′= χ ′ for every multigraph, is… Expand

A proper vertex coloring of a graph is equitable if the sizes of its color classes differ by at most one. In this paper, we prove that if G is a graph such that for each edge [email protected]?E(G),… Expand

Given lists of available colors assigned to the vertices of a graph G, a list coloring is a proper coloring of G such that the color on each vertex is chosen from its list. If the lists all have size… Expand

While solving a question on the list coloring of planar graphs, Dvořák and Postle introduced the new notion of DP-coloring (they called it correspondence coloring). A DP-coloring of a graph G reduces… Expand