Showing papers in "Discrete Mathematics in 2018"

TL;DR: On graphs of maximal edge dimension and on a conjectured upper bound of the ratio between $\mathrm{edim}(G)$ and $\dim(G), which is the standard metric dimension of $G$ are answered.

TL;DR: A Dyck path model for unit-interval graphs is used to study the chromatic quasisymmetric functions introduced by Shareshian and Wachs, as well as unicellular LLT polynomials, revealing some parallel structure and phenomena regarding their e -positivity.

TL;DR: It is shown that for every fixed k and g ≥ 2 k + 2 , almost every n -vertex cubic graph of girth at least g has the packing chromatic number greater than k.

TL;DR: In this article, the authors showed that for each k ∈ { 3, 4, 5, 6 }, every planar graph without C k is 4-DP-colorable, which is an extension of the above results.

TL;DR: This paper proposes a conjecture concerning partial sums of an arbitrary finite subset of an abelian group, that naturally arises investigating simple Heffter systems and shows its connection with related open problems and presents some results about the validity of these conjectures.

TL;DR: A simple framework for constructing de Bruijn sequences, and more generally, universal cycles, via successor rules, is presented, based on the often used method of joining disjoint cycles.

TL;DR: Using some transformations, a sharp lower bound is got on Steiner k -Wiener index for trees with given diameter, and the corresponding extremal graph is obtained as well.

TL;DR: This note presents an explicit infinite family of subcubic graphs with unbounded packing chromatic number in the class of graphs with maximum degree $3$.

TL;DR: This paper provides a combinatorial description of det ( L ( G ) ) that generalizes that for the determinant of the Laplacian matrix of a signed graph.

TL;DR: It is shown that the linear sets of pseudoregulus type and for t ≥ 4 the scattered linear sets found by Lunardon and Polverino are the only maximum scattered F q -linear sets in PG.

TL;DR: It is shown that for any fixed integers m ≥ 2 and t ≥ 2 , the star-critical Ramsey number r ∗ ( K 1 + n K t , K m + 1 ) = ( m − 1 ) t n + t for all sufficiently large n.

TL;DR: It is shown that the number of Aut ( Y ) -orbits of vertices for any semi-equivelar map Y on the torus is at most six except one type of semi-Equivelar maps.

TL;DR: In this paper, it was shown that the DP-chromatic number differs from the list chromatic number in the sense that t ≥ 1 + (k k ∕ k! ) (log (k! ) + 1 ).

TL;DR: The descent polynomials of separable permutations and derangements are both demonstrated to be unimodal and it is proved that the γ -coefficients of the first are positive with an interpretation parallel to the classical Eulerian polynomial.

TL;DR: The natural extension in which the cop probes a set of k vertices, rather than a single vertex, at each turn is considered, which gives an asymptotically best-possible linear bound in one direction and shows that in the other direction no subexponential bound holds.

TL;DR: In this article, the authors provided new injective proofs of the Erdős-Ko-Rado and the Hilton-Milner theorems, which was proved as part of a stronger result by Hilton and Milner.

TL;DR: The aim of this paper is to establish all self-dual -constacyclic codes of length ps over the finite commutative chain ring R=Fpm+uFpm, where p is a prime and u2=0.

TL;DR: It is proved that three colors are sufficient to produce a multi-set neighbor distinguishing edge coloring for every graph without isolated edges.

TL;DR: In this paper, the authors gave explicit characterizations of all sequences S of G such that |S | = D (G ) − 1 and S is free of subsequences whose product is 1, where G is equal to D 2 n or Q 4 n for some n.

TL;DR: In this paper, the maximum number of hyperedges possible in an r -uniform, connected n -vertex hypergraph without a Berge path of length k is asymptotically determined.

TL;DR: A stability theorem is complete which strengthens Kopylov’s result that for k ≥ 3 odd and all n ≥ k, every n -vertex 2-connected graph G with no cycle of length at least k is a subgraph of one of the two extremal graphs.

TL;DR: In this article, the cop-throttling number of a graph G for the game of Cops and Robbers is defined to be the minimum of (k + capt k (G ) ), where k is the number of cops and capt k(G ) is the minimum number of rounds needed for k cops to capture the robber on G over all possible games.

TL;DR: The first direct bijective proof of Amdeberhan's conjecture was given in this article by establishing a bijection between the set of ( s, s + 2 ) -core partitions with distinct parts and a set of lattice paths.

TL;DR: These algorithms are based on the results that triangle-free odd-signable graphs have treewidth at most 5 and thus have clique-width at most 48, and that (cap, 4-hole)-free even-hole-free graphs G without clique cutsets have treelined at most 6 ω ( G ) − 1 and clique

TL;DR: In this paper, it was shown that the infinite matroid intersection conjecture of Nash-Williams implies the infinite Menger theorem proved by Aharoni and Berger in 2009, and that this conjecture is true whenever one matroid is nearly finitary and the second is the dual of a nearly-finitary matroid.

TL;DR: The first author is supported by a Research Incentive Grant from The Carnegie Trust for the Universities of Scotland (Grant No. 70582) as mentioned in this paper, and the second author was supported by the University of Edinburgh.

TL;DR: A short proof of Kriesell’s Conjecture is given and it is shown that λ k ( G) ≥ 1 k − 1 k l 2 if λ ( G ) ≥ l in G, where k = 3, 4 .

TL;DR: The Ramsey number for the 3-path of length three and $n$ colors is studied and it is shown that $R(P^3_3;n)le \lambda_0 n+7\sqrt{n}$, for some explicit constant $\ lambda_0=1.97466\dots$.

TL;DR: A new method is shown to prove real-rootedness of the independence polynomials of certain families of trees and of centipedes, caterpillars, and Zhu’s theorem.

TL;DR: Verifying a conjecture of Brewster, Foucaud, Hell and Naserasr, it is shown that signed ( H, Π ) -colouring is NP-complete for any signed graph whose s-core has at least 3 edges.