Search Results - "Kostochka, A.V."

List Edge and List Total Colourings of Multigraphs by Borodin, O.V., Kostochka, A.V., Woodall, D.R.

“…This paper exploits the remarkable new method of Galvin (J. Combin. Theory Ser. B63(1995), 153–158), who proved that the list edge chromatic numberχ′list(G) of…”
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Defective 2-colorings of sparse graphs by Borodin, O.V., Kostochka, A.V.

“…A graph G is (j,k)-colorable if its vertices can be partitioned into subsets V1 and V2 such that every vertex in G[V1] has degree at most j and every vertex in…”
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Ks,t Minors in (s+t)- Chromatic Graphs, II by Kostochka, A.V.

“…Let Ks,t* denote the graph obtained from the complete graph Ks+t by deleting the edges of some Kt‐subgraph. The author proved earlier that for each fixed s and…”
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Minors in ‐ Chromatic Graphs, II by Kostochka, A.V.

“…Let denote the graph obtained from the complete graph by deleting the edges of some ‐subgraph. The author proved earlier that for each fixed s and , every…”
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Strong chromatic index of subcubic planar multigraphs by Kostochka, A.V., Li, X., Ruksasakchai, W., Santana, M., Wang, T., Yu, G.

“…The strong chromatic index of a multigraph is the minimum k such that the edge set can be k-colored requiring that each color class induces a matching. We…”
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On K s , t -minors in graphs with given average degree, II by Kostochka, A.V., Prince, N.

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Coloring Relatives of Intervals on the Plane, I: Chromatic Number Versus Girth by Kostochka, A.V., Nešetřil, J.

“…For the intersection graphs of intervals, rays and strings on the plane, we estimate maximum chromatic number in terms of girth…”
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On the Corrádi–Hajnal theorem and a question of Dirac by Kierstead, H.A., Kostochka, A.V., Yeager, E.C.

“…In 1963, Corrádi and Hajnal proved that for all k≥1 and n≥3k, every graph G on n vertices with minimum degree δ(G)≥2k contains k disjoint cycles. The bound…”
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On Ks,t-minors in graphs with given average degree, II by Kostochka, A.V., Prince, N.

“…Let Ks,t∗ denote the graph obtained from Ks,t by adding all edges between the s vertices of degree t in it. We show how to adapt the argument of our previous…”
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Dense graphs have K 3 , t minors by Kostochka, A.V., Prince, N.

“…Let K 3 , t ∗ denote the graph obtained from K 3 , t by adding all edges between the three vertices of degree t in it. We prove that for each t ≥ 6300 and n ≥…”
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An Ore-type theorem on equitable coloring by Kierstead, H.A., Kostochka, A.V.

“…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…”
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On a packing problem of Alon and Yuster by Kostochka, A.V., McConvey, A., Yager, D.

“…Two graphs G1 and G2, each on n vertices, pack if there exists a bijection f from V(G1) onto V(G2) such that uv∈E(G1) only if f(u)f(v)∉E(G2). In 2014, Alon and…”
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The minimum number of edges in a 4-critical graph that is bipartite plus 3 edges by Kostochka, A.V., Reiniger, B.M.

“…Rödl and Tuza proved that sufficiently large (k+1)-critical graphs cannot be made bipartite by deleting fewer than (k2) edges, and that this is sharp. Chen,…”
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Describing faces in plane triangulations by Borodin, O.V., Ivanova, A.O., Kostochka, A.V.

“…Lebesgue (1940) proved that every plane triangulation contains a face with the vertex-degrees majorized by one of the following triples:…”
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Describing 3-paths in normal plane maps by Borodin, O.V., Ivanova, A.O., Jensen, T.R., Kostochka, A.V., Yancey, M.P.

“…We prove that every normal plane map, as well as every 3-polytope, has a path on three vertices whose degrees are bounded from above by one of the following…”
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An upper bound on the domination number of n -vertex connected cubic graphs by Kostochka, A.V., Stodolsky, B.Y.

“…In 1996, Reed proved that the domination number γ ( G ) of every n -vertex graph G with minimum degree at least 3 is at most 3 n / 8 . This bound is sharp for…”
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Large minors in graphs with given independence number by Balogh, József, Kostochka, A.V.

“…A weakening of Hadwiger’s conjecture states that every n-vertex graph with independence number α has a clique minor of size at least nα. Extending ideas of Fox…”
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Ore-type versions of Brooks' theorem by Kierstead, H.A., Kostochka, A.V.

“…The Ore-degree of an edge xy in a graph G is the sum θ ( x y ) = d ( x ) + d ( y ) of the degrees of its ends. In this paper we discuss colorings and equitable…”
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Coloring uniform hypergraphs with few edges by Kostochka, A.V., Kumbhat, M.

“…A hypergraph is b‐simple if no two distinct edges share more than b vertices. Let m(r, t, g) denote the minimum number of edges in an r‐uniform non‐t‐colorable…”
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Constructions of sparse uniform hypergraphs with high chromatic number by Kostochka, A.V., Rödl, V.

“…A random construction gives new examples of simple hypergraphs with high chromatic number that have few edges and/or low maximum degree. In particular, for…”
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