A linear pseudo-Boolean viewpoint on matching and other central concepts in graph theory
A Linear Time Algorithm for Computing Longest Paths in Cactus Graphs
ACM Computing Classification System (1998): G.2.2.We propose an algorithm that computes the length of a longest path in a cactus graph. Our algorithm can easily be modified to output a longest path as well or to solve the problem on cacti with edge or vertex weights. The algorithm works on rooted cacti and assigns to each vertex a two-number label, the first number being the desired parameter of the subcactus rooted at that vertex. The algorithm applies the divide-and-conquer approach and computes...
A linear upper bound in zero-sum Ramsey theory.
A Link Between Ordered Sets And Trees On The Rectangle Tree Hypothesis
A Little bijection for affine Stanley symmetric functions.
A Littlewood-Richardson rule for evaluation representations of .
A local limit theorem for the critical random graph.
A local minimum energy condition of hexagonal circle packing.
A Loopless Implementation of a Gray Code for Signed Permutations
A lower bound for Schur numbers and multicolor Ramsey numbers.
A lower bound for the arithmetical complexity of Sturmian words.
A lower bound for the irredundance number of trees
Let ir(G) and γ(G) be the irredundance number and domination number of a graph G, respectively. The number of vertices and leaves of a graph G are denoted by n(G) and n₁(G). If T is a tree, then Lemańska [4] presented in 2004 the sharp lower bound γ(T) ≥ (n(T) + 2 - n₁(T))/3. In this paper we prove ir(T) ≥ (n(T) + 2 - n₁(T))/3. for an arbitrary tree T. Since γ(T) ≥ ir(T) is always valid, this inequality is an extension and improvement of Lemańska's result. ...
A lower bound for the number of distinct eigenvalues of some real symmetric matrices.
A lower bound for the number of edges in a graph containing no two cycles of the same length.
A Lower Bound for the Optimal Crossing-Free Hamiltonian Cycle Problem.
A lower bound for the packing chromatic number of the Cartesian product of cycles
Let G = (V, E) be a simple graph of order n and i be an integer with i ≥ 1. The set X i ⊆ V(G) is called an i-packing if each two distinct vertices in X i are more than i apart. A packing colouring of G is a partition X = {X 1, X 2, …, X k} of V(G) such that each colour class X i is an i-packing. The minimum order k of a packing colouring is called the packing chromatic number of G, denoted by χρ(G). In this paper we show, using a theoretical proof, that if q = 4t, for some integer t ≥ 3, then 9...
A lower bound on the independence number of a graph in terms of degrees
For a connected and non-complete graph, a new lower bound on its independence number is proved. It is shown that this bound is realizable by the well known efficient algorithm MIN.
A Macdonald vertex operator and standard tableaux statistics for the two-column -Kosta coefficients.
A magical approach to some labeling conjectures
In this paper, a complete characterization of the (super) edge-magic linear forests with two components is provided. In the process of establishing this characterization, the super edge-magic, harmonious, sequential and felicitous properties of certain 2-regular graphs are investigated, and several results on super edge-magic and felicitous labelings of unions of cycles and paths are presented. These labelings resolve one conjecture on harmonious graphs as a corollary, and make headway towards the...
A Marica-Schönheim Theorem for an Infinite Sequence of Finite Sets.