
Upper bounds for inverse domination in graphs
In any graph G, the domination number γ(G) is at most the independence n...
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On graphs with no induced fivevertex path or paraglider
Given two graphs H_1 and H_2, a graph is (H_1, H_2)free if it contains ...
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Bounding the number of edges of matchstick graphs
We show that a matchstick graph with n vertices has no more than 3nc√(n...
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On tradeoffs between width and filllike graph parameters
In this work we consider two twocriteria optimization problems: given a...
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Shifted varieties and discrete neighborhoods around varieties
For an affine variety X defined over a finite prime field F_p and some i...
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MaxCut in Degenerate HFree Graphs
We obtain several lower bounds on the MaxCut of ddegenerate Hfree gra...
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Dynamic Averaging Load Balancing on Cycles
We consider the following dynamic loadbalancing process: given an under...
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Making an HFree Graph kColorable
We study the following question: how few edges can we delete from any Hfree graph on n vertices in order to make the resulting graph kcolorable? It turns out that various classical problems in extremal graph theory are special cases of this question. For H any fixed odd cycle, we determine the answer up to a constant factor when n is sufficiently large. We also prove an upper bound when H is a fixed clique that we conjecture is tight up to a constant factor, and prove upper bounds for more general families of graphs. We apply our results to get a new bound on the maximum cut of graphs with a forbidden odd cycle in terms of the number of edges.
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