Unavoidable chromatic patterns in 2‐colorings of the complete graph
Given a graph G on k edges, we consider the following two extremal problems: provided n is
large enough, what is the minimum integer bal (n, G), if it exists, such that any 2‐coloring of …
large enough, what is the minimum integer bal (n, G), if it exists, such that any 2‐coloring of …
On zero-sum spanning trees and zero-sum connectivity
We consider $2 $-colourings $ f: E (G)\rightarrow\{-1, 1\} $ of the edges of a graph $ G $ with
colours $-1$ and $1 $ in $\mathbb {Z} $. A subgraph $ H $ of $ G $ is said to be a zero-sum …
colours $-1$ and $1 $ in $\mathbb {Z} $. A subgraph $ H $ of $ G $ is said to be a zero-sum …
On the balanceability of some graph classes
A Dailly, A Hansberg, D Ventura - Discrete Applied Mathematics, 2021 - Elsevier
Given a graph G, a 2-coloring of the edges of K n is said to contain a balanced copy of G if
we can find a copy of G such that half of its edges are in each color class. If, for every …
we can find a copy of G such that half of its edges are in each color class. If, for every …
On small balanceable, strongly-balanceable and omnitonal graphs
In Ramsey theory for graphs we are given a graph $ G $ and we are required to find the
least $ n_0 $ such that, for any $ n\geq n_0 $, any red/blue colouring of the edges of $ K_n …
least $ n_0 $ such that, for any $ n\geq n_0 $, any red/blue colouring of the edges of $ K_n …
A uniform bound on almost colour-balanced perfect matchings in colour-balanced cliques
L Hollom - arXiv preprint arXiv:2410.07993, 2024 - arxiv.org
An edge-colouring of a graph $ G $ is said to be colour-balanced if there are equally many
edges of each available colour. We are interested in finding a colour-balanced perfect …
edges of each available colour. We are interested in finding a colour-balanced perfect …
On Katznelson's Question for skew-product systems
D Glasscock, A Koutsogiannis, F Richter - Bulletin of the American …, 2022 - ams.org
Katznelson's Question is a long-standing open question concerning recurrence in
topological dynamics with strong historical and mathematical ties to open problems in …
topological dynamics with strong historical and mathematical ties to open problems in …
On the existence of zero-sum perfect matchings of complete graphs
T Kittipassorn, P Sinsap - arXiv preprint arXiv:2011.00862, 2020 - arxiv.org
In this paper, we prove that given a 2-edge-coloured complete graph $ K_ {4n} $ that has the
same number of edges of each colour, we can always find a perfect matching with an equal …
same number of edges of each colour, we can always find a perfect matching with an equal …
The Effect of Local Majority on Global Majorityin Connected Graphs
Let\mathcal GG be an infinite family of connected graphs and let k be a positive integer. We
say that k is forcing for\mathcal GG if for all G ∈\mathcal GG∈ G but finitely many, the …
say that k is forcing for\mathcal GG if for all G ∈\mathcal GG∈ G but finitely many, the …
Zero-sum squares in bounded discrepancy {-1, 1}-matrices
AR Arévalo, A Montejano… - arXiv preprint arXiv …, 2020 - arxiv.org
For $ n\ge 5$, we prove that every $ n\times n $ matrix $ M=(a_ {i, j}) $ with entries in $\{-1,
1\} $ and absolute discrepancy $|\mathrm {disc}(M)|=|\sum a_ {i, j}|\le n $ contains a zero …
1\} $ and absolute discrepancy $|\mathrm {disc}(M)|=|\sum a_ {i, j}|\le n $ contains a zero …
The balancing number and list balancing number of some graph classes
Given a graph $ G $, a 2-coloring of the edges of $ K_n $ is said to contain a balanced copy
of $ G $ if we can find a copy of $ G $ such that half of its edges is in each color class. If there …
of $ G $ if we can find a copy of $ G $ such that half of its edges is in each color class. If there …