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- Alexandr V. Kostochka
- Combinatorica
- 1984

Let us recall the notion of the Hadwiger number. The following operations are called elementary contractions: substitution of two adjacent points vl and v~ for a new point vs connected to the pointsâ€¦ (More)

- Oleg V. Borodin, Alexandr V. Kostochka
- J. Comb. Theory, Ser. B
- 1977

- Oleg V. Borodin, Alexandr V. Kostochka, Douglas R. Woodall
- J. Comb. Theory, Ser. B
- 1997

This paper exploits the remarkable new method of Galvin (J. Combin. Theory Ser. B 63 (1995), 153 158), who proved that the list edge chromatic number /$list(G) of a bipartite multigraph G equals itsâ€¦ (More)

- Alexandr V. Kostochka, Douglas R. Woodall
- Discrete Mathematics
- 2001

This paper starts with a discussion of several old and new conjectures about choosability in graphs. In particular, the list-colouring conjecture, that châ€² = â€² for every multigraph, is shown to implyâ€¦ (More)

- Hal A. Kierstead, Alexandr V. Kostochka
- Combinatorics, Probability & Computing
- 2008

An equitable k-colouring of a graph G is a proper k-colouring, for which any two colour classes differ in size by at most one. Equitable colourings naturally arise in some scheduling, partitioning,â€¦ (More)

- Hal A. Kierstead, Alexandr V. Kostochka
- J. Comb. Theory, Ser. B
- 2008

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 xy âˆˆ E(G), the sum d(x)â€¦ (More)

- Peter Hamburger, Penny E. Haxell, Alexandr V. Kostochka
- Electr. J. Comb.
- 2007

Using a recent result of Chudnovsky, Seymour, and Sullivan, we slightly improve two bounds related to the Caccetta-Haggkvist Conjecture. Namely, we show that if Î± â‰¥ 0.35312, then each n-vertexâ€¦ (More)

- Alexandr V. Kostochka, Matthew P. Yancey
- J. Comb. Theory, Ser. B
- 2014

A graph G is k-critical if it has chromatic number k, but every proper subgraph of G is (kâˆ’ 1)â€“colorable. Let fk(n) denote the minimum number of edges in an n-vertex k-critical graph. We give a lowerâ€¦ (More)

- Alexandr V. Kostochka, Vojtech RÃ¶dl
- Journal of Graph Theory
- 2001

Let R (G) denote the minimum integer N such that for every bicoloring of the edges of KN, at least one of the monochromatic subgraphs contains G as a subgraph. We show that for every positive integerâ€¦ (More)

- Alexandr V. Kostochka, LÃ¡szlÃ³ Pyber
- Combinatorica
- 1988