On the discrepancies of graphs

26 Feb 2020  ·  Balogh József, Csaba Béla, Jing Yifan, Pluhár András ·

In the literature, the notion of discrepancy is used in several contexts, even in the theory of graphs. Here, for a graph $G$, $\{-1, 1\}$ labels are assigned to the edges, and we consider a family $\mathcal{S}_G$ of (spanning) subgraphs of certain types, among others spanning trees, Hamiltonian cycles... As usual, we seek for bounds on the sum of the labels that hold for all elements of $\mathcal{S}_G$, for every labeling. read more

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Combinatorics