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pro vyhledávání: '"Timmons, Craig"'
Let $R$ be a ring. The unitary addition Cayley graph of $R$, denoted $\mathcal{U}(R)$, is the graph with vertex $R$, and two distinct vertices $x$ and $y$ are adjacent if and only if $x+y$ is a unit. We determine a formula for the clique number and c
Externí odkaz:
http://arxiv.org/abs/2407.10364
In this paper, we study the maximum number of edges in an $N$-vertex $r$-uniform hypergraph with girth $g$ where $g \in \{5,6 \}$. Writing $\textrm{ex}_r ( N, \mathcal{C}_{
Externí odkaz:
http://arxiv.org/abs/2404.01839
Autor:
Taranchuk, Vladislav, Timmons, Craig
A complete partition of a graph $G$ is a partition of the vertex set such that there is at least one edge between any two parts. The largest $r$ such that $G$ has a complete partition into $r$ parts, each of which is an independent set, is the achrom
Externí odkaz:
http://arxiv.org/abs/2311.10379
A graph is called an $(r,k)$-graph if its vertex set can be partitioned into $r$ parts of size at most $k$ with at least one edge between any two parts. Let $f(r,H)$ be the minimum $k$ for which there exists an $H$-free $(r,k)$-graph. In this paper w
Externí odkaz:
http://arxiv.org/abs/2308.16728
Autor:
Taranchuk, Vladislav, Timmons, Craig
Publikováno v:
In Finite Fields and Their Applications October 2024 99
Autor:
Davini, David, Timmons, Craig
Gerbner, Patk\'{o}s, Tuza, and Vizer recently initiated the study of $F$-saturated regular graphs. One of the essential problems in this line of research is determining when such a graph exists. Using generalized sum-free sets we prove that for any o
Externí odkaz:
http://arxiv.org/abs/2108.13406
A subset $A$ of the integers is a $B_k[g]$ set if the number of multisets from $A$ that sum to any fixed integer is at most $g$. Let $F_{k,g}(n)$ denote the maximum size of a $B_k[g]$ set in $\{1,\dots, n\}$. In this paper we improve the best-known u
Externí odkaz:
http://arxiv.org/abs/2105.03706
Autor:
Timmons, Craig
In a recent paper, Gerbner, Patk\'{o}s, Tuza and Vizer studied regular $F$-saturated graphs. One of the essential questions is given $F$, for which $n$ does a regular $n$-vertex $F$-saturated graph exist. They proved that for all sufficiently large $
Externí odkaz:
http://arxiv.org/abs/2103.08831
A graph $G$ is $F$-saturated if it contains no copy of $F$ as a subgraph but the addition of any new edge to $G$ creates a copy of $F$. We prove that for $s \geq 3$ and $t \geq 2$, the minimum number of copies of $K_{1,t}$ in a $K_s$-saturated graph
Externí odkaz:
http://arxiv.org/abs/2101.00507
Autor:
Tait, Michael, Timmons, Craig
Let $\mathrm{rex}(n, F)$ denote the maximum number of edges in an $n$-vertex graph that is regular and does not contain $F$ as a subgraph. We give lower bounds on $\mathrm{rex}(n, F)$, that are best possible up to a constant factor, when $F$ is one o
Externí odkaz:
http://arxiv.org/abs/2005.02907