Showing papers in "Journal of Combinatorial Theory, Series B in 2022"

TL;DR: In this paper , it was shown that |F| ≥ (nk)−(n−sk), provided n≥53sk−23s and s is sufficiently large.

TL;DR: In this article , it was shown that if a graph has treewidth at least f(k,d) and maximum degree at most d, then it contains a k×k-grid as an induced minor.

TL;DR: In this article , it was shown that if G has the maximum spectral radius among all n-vertex graphs not containing G, then G is a member of Ex(n,F) for n large enough, then Cioabă, Desai and Tait's conjecture is completely solved.

TL;DR: In this article , it was shown that there is a digraph with bounded clique number, large dichromatic number, and no induced directed cycles of odd length at least 5.

TL;DR: In this article , it was shown that χs′(G)≤1.835Δ(G), which is the same result for ε ≥ 1/26.

TL;DR: For graphs with bounded treewidth, the maximum chromatic number of such graphs is Θ(s^2/log s) as discussed by the authors , where s is the number of edges in a graph that can be subdivided more than once.

TL;DR: In this article , it was shown that for sufficiently large Δ, if G is a graph with maximum degree at most Δ and no clique of size ω , then χ ( G ) ≤ 72 Δ ln ⁡ ( ω ) ln ln ω ln ε ln ∈ V (G ) , | L ( v ) | ≥ 72 deg ‡ ( v) ⋅ min { ln ǫ ( v ǵ ) lln à ǔ ( deg ǒ ( v ), log 2 † ( χ ǝ ( vǫ + 1) lnǫ ln nǫ n ∞ ln gǫ ) lǫ ǡ ( deg ) Ǫ Ǡ ( v )) , where χ n denotes the chromatic number of the neighborhood of v and g denotes the size of a largest clique.

TL;DR: In this article , a comprehensive set of q-matroid axiom systems and a cryptomorphism between them and classical matroid cryptomorphisms are established. But the difference between classical theory and its q-analogue is highlighted.

TL;DR: In this paper , the authors give a proof of Thomassen's conjecture by building a pillar (algorithmically) in sublinear expanders, which is a graph that consists of two vertex-disjoint cycles of the same length.

TL;DR: In this article, the first deterministic distributed edge-coloring algorithm that uses only Δ + 1 colors was presented, which matches the bound given by Vizing's theorem and is inspired by the recent proof of Grebik and Pikhurko's theorem.

TL;DR: In this paper , it was shown that if a digraph F is an orientation of a cycle, then mader χ → (F ) = v (F ), which is the smallest integer k such that every k -dichromatic digraph contains a subdivision of F .

TL;DR: In this paper, the range of the Turan numbers for edge blow-up of all bipartite graphs and the exact Turan number for all non-bipartite graph was determined.

TL;DR: Chudnovsky, Scott, and Seymour as discussed by the authors showed that C ⩾ t -free graphs are χ-bounded, i.e., graphs that exclude induced cycles with at least t vertices.

TL;DR: An infinite family of Praeger-Xu graphs is constructed in which a smallest vertex-transitive group of symmetries has arbitrarily large vertex-stabiliser.

TL;DR: In this article , it was shown that the average order of a connected induced subgraph over all connected graphs is minimised by the path P n , and the main result of this conjecture was confirmed.

TL;DR: In this article, the exact structure of the extremal trees with sufficiently many vertices is described and the structure evolves when the number of vertices grows, and it is shown that γ n = 1 365 1 53 (1 + 26 55 + 156 106 ) n + O ( 1 ) ≈ 0.67737178 n + o( 1 ).

TL;DR: In this article, a simple combinatorial description of an (n − 2 k + 2 ) -chromatic edge-critical subgraph of the Schrijver graph SG (n, k ) is given.

TL;DR: In this paper , it was shown that every graph has a canonical tree of tree-decompositions that distinguishes all principal tangles (these include the ends and various kinds of large finite dense structures) efficiently.

TL;DR: In this paper, it was shown that if a digraph F is an orientation of a cycle, then mader χ → (F ) = v (F ), which is the smallest integer k such that every k-dichromatic digraph contains a subdivision of F.

TL;DR: In this paper , the exact structure of the extremal trees with sufficiently many vertices is described and the structure evolves when the number of vertices grows, and it is shown that γn=1365153(1+2655+156106)n+O(1)≈ 0.67737178n+ O(1).

TL;DR: In this paper , the maximum spectral radius of Ks,t-minor free graphs of sufficiently large order was determined for t ≥ 1 and t ≥ 2, and the result completely solves Tait's conjecture.

TL;DR: Recently, Liu and Montgomery confirmed Thomassen's conjecture, but the optimal bound on d(k) still remains open as discussed by the authors , which is the best known bound for a k-subdivision.

TL;DR: In this article , the problem of minimizing submodular functions on the product of diamonds of finite size is reduced to the membership problem for an associated polyhedron, which is equivalent to the optimization problem over the polyhedra, based on the ellipsoid method.

TL;DR: In this paper , it was shown that any quasirandom dense large graph in which all degrees are equal and even can be decomposed into any given collection of two-factors (2-regular spanning subgraphs).

TL;DR: In this article , the range of the Turán number for edge blow-up of all bipartite graphs and the exact Turán numbers for all non-bipartite graph was determined.

TL;DR: A graph H is common if the number of monochromatic copies of H in a 2-edge-colouring of the complete graph Kn is asymptotically minimised by the random colouring as discussed by the authors .

TL;DR: In this paper , the authors give a description of many new jumps in the possible speeds of a hereditary L-property, where L is any finite relational language, and characterize the jumps in polynomial and factorial ranges, and show they are essentially the same as in the case of graphs.

TL;DR: In this paper, it was shown that the average order of a connected induced subgraph over all connected graphs is minimised by the path P n, and the main result of this conjecture was confirmed.

TL;DR: For any even integer k ≥ 6, integer d such that k/2≤d≤k−1, and sufficiently large n∈(k/2)N, the degree condition coincides with the one for the existence of perfect matchings provided by Rödl, Ruciński and Szemerédi as mentioned in this paper .

TL;DR: In this paper , it was shown that all trees are ubiquitous with respect to the topological minor relation, irrespective of their cardinality, which is the same as the answer of Andreae from 1979.