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Turan Problems and Shadows III: expansions of graphs
Alexandr Kostochka, Dhruv Mubayi, Jacques Verstraete
The expansion of a graph is the -uniform hypergraph obtained from by enlarging each edge of with a new vertex disjoint from such that distinct edges are…
On Coupon Colorings of Graphs
Bob Chen, Jeong Han Kim, Michael Tait +1
Let be a graph with no isolated vertices. A {\em -coupon coloring} of is an assignment of colors from to the vertices of such that the neigh…
On sets of integers with restrictions on their products
Michael Tait, Jacques Verstraete
A {\em product-injective labeling} of a graph is an injection such that for any distinct edges . Let b…
Cycles in triangle-free graphs of large chromatic number
Alexandr Kostochka, Benny Sudakov, Jacques Verstraete
More than twenty years ago Erdős conjectured~\cite{E1} that a triangle-free graph of chromatic number contains cycles of at least $k^{2 - \varepsilon}…
Turan Problems and Shadows II: Trees
Alexandr Kostochka, Dhruv Mubayi, Jacques Verstraete
The expansion of a graph is the 3-uniform hypergraph obtained from by enlarging each edge of with a vertex disjoint from such that distinct edges are enlar…