Results 51 to 60 of about 24,599 (177)

The k-Ramsey number of two five cycles

AKCE International Journal of Graphs and Combinatorics
Given any two graphs F and H, the Ramsey number R(F, H) is defined as the smallest positive integer n such that every red-blue coloring of the edges of the complete graph Kn of order n, there will be a subgraph of Kn isomorphic to F whose edges are all ...
Johannes H. Hattingh, Elizabeth Jonck, Ronald J. Maartens   +2 more
doaj   +1 more source

An efficient container lemma

Discrete Analysis, 2020
An efficient container lemma, Discrete Analysis 2020:17, 56 pp. The hypergraph container lemma, discovered independently in 2012 by David Saxton and Andrew Thomason, and by József Balogh, Robert Morris and Wojciech Samotij, is an extremely powerful tool
Jozsef Balogh, Wojciech Samotij
doaj   +1 more source

Ore‐Type Conditions for Existence of a Jellyfish in a Graph

Journal of Graph Theory, Volume 111, Issue 4, Page 124-143, April 2026.
ABSTRACT The famous Dirac's theorem states that for each n ≥ 3 every n‐vertex graph G with minimum degree δ ( G ) ≥ n / 2 has a Hamiltonian cycle. When δ ( G ) < n / 2, this cannot be guaranteed, but the existence of some other specific subgraphs can be provided.
Jaehoon Kim, Alexandr Kostochka, Ruth Luo   +2 more
wiley   +1 more source

Recoloring via Modular Decomposition

Journal of Graph Theory, Volume 111, Issue 4, Page 113-123, April 2026.
ABSTRACT The reconfiguration graph of the k‐colorings of a graph G, denoted R k ( G ), is the graph whose vertices are the k‐colorings of G and two colorings are adjacent in R k ( G ) if they differ in color on exactly one vertex. A graph G is said to be recolorable if R ℓ ( G ) is connected for all ℓ ≥ χ ( G ) + 1.
Manoj Belavadi, Kathie Cameron, Ni Luh Dewi Sintiari   +2 more
wiley   +1 more source

Random graphs containing arbitrary distributions of subgraphs

, 2010
Traditional random graph models of networks generate networks that are locally tree-like, meaning that all local neighborhoods take the form of trees. In this respect such models are highly unrealistic, most real networks having strongly non-tree-like ...
Brian Karrer, D. Mollison, J. Harris, M. E. J. Newman, M. Penrose, P. Erdős, P. Erdős   +6 more
core   +1 more source

Tractable but Hard to Approximate: The Bi‐Objective Minimum s$$ s $$‐t$$ t $$‐Cut Problem With Binary Capacities

Networks, Volume 87, Issue 3, Page 312-321, April 2026.
ABSTRACT The minimum s$$ s $$‐t$$ t $$‐cut problem is one of the most‐studied problems in discrete optimization and has a unique complexity status in multi‐objective optimization. Even though the single‐objective version of the problem can be solved in polynomial time, it has been shown in the seminal work of Papadimitriou and Yannakakis (2000) that ...
Jan Boeckmann, Stephan Helfrich, Oliver Bachtler, Stefan Ruzika, Clemens Thielen   +4 more
wiley   +1 more source

A note on the minimum rank of graphs with given dominating induced subgraph

The American Journal of Combinatorics
An induced subgraph of a graph \(G\) is said to be dominating if every vertex of \(G\) is at distance at most one from this subgraph. We investigate pairs \((G, F)\) where \(F\) is a non-singular dominating induced subgraph of \(G,\) and the rank of \(G\
Zoran Stanić
doaj   +1 more source

Perfect Matching Under Precedence Constraints

Networks, Volume 87, Issue 2, Page 175-190, March 2026.
ABSTRACT In this article, we motivate and define variants of perfect matching under precedence constraints where a perfect matching is built incrementally and precedence constraints ensure that an edge may only be added to the matching if the edge's predecessor vertices have already been covered.
Christina Büsing, Corinna Mathwieser
wiley   +1 more source

Small clique number graphs with three trivial critical ideals [PDF]

, 2013
The critical ideals of a graph are the determinantal ideals of the generalized Laplacian matrix associated to a graph. In this article we provide a set of minimal forbidden graphs for the set of graphs with at most three trivial critical ideals.
Carlos, Carlos A. Alfaro, E. Valencia
core  

Solving a Random Asymmetric TSP Exactly in Quasi‐Polynomial Time W.H.P.

Random Structures &Algorithms, Volume 68, Issue 2, March 2026.
ABSTRACT Let the costs C(i,j)$$ C\left(i,j\right) $$ for an instance of the Asymmetric Traveling Salesperson Problem (ATSP) be independent copies of a nonnegative random variable C$$ C $$ from a class of distributions that include the uniform [0,1]$$ \left[0,1\right] $$ distribution and the exponential mean 1 distribution with mean 1.
Tolson Bell, Alan M. Frieze
wiley   +1 more source