
On sublinear approximations for the Petersen coloring conjecture
If f:ℕ→ℕ is a function, then let us say that f is sublinear if lim_...
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Cuts in matchings of 3edgeconnected cubic graphs
We discuss relations between several known (some false, some open) conje...
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Normal edgecolorings of cubic graphs
A normal kedgecoloring of a cubic graph is an edgecoloring with k col...
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Nondeterminisic Sublinear Time Has Measure 0 in P
The measure hypothesis is a quantitative strengthening of the P != NP co...
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Coloring Drawings of Graphs
We consider facecolorings of drawings of graphs in the plane. Given a m...
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A power APN function CCZequivalent to Kasami function in even dimension
Let n be an even number such that n≡ 0 4. We show that a power function ...
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On two consequences of BergeFulkerson conjecture
The classical BergeFulkerson conjecture states that any bridgeless cubi...
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Sublinear bounds for nullity of flows and approximating Tutte's flow conjectures
A function f:N→ N is sublinear, if lim_x→ +∞f(x)/x=0. If A is an Abelian group, G is a graph and ϕ is an Aflow in G, then let N(ϕ) be the nullity of ϕ, that is, the set of edges e of G with ϕ(e)=0. In this paper we show that (a) Tutte's 5flow conjecture is equivalent to the statement that there is a sublinear function f, such that all 3edgeconnected cubic graphs admit a ℤ_5flow ϕ (not necessarily nowhere zero), such that N(ϕ)≤ f(E(G)); (b) Tutte's 4flow conjecture is equivalent to the statement that there is a sublinear function f, such that all bridgeless graphs without a Petersen minor admit a ℤ_4flow ϕ (not necessarily nowhere zero), such that N(ϕ)≤ f(E(G)); (c) Tutte's 3flow conjecture is equivalent to the statement that there is a sublinear function f, such that all 4edgeconnected graphs admit a ℤ_3flow ϕ (not necessarily nowhere zero), such that N(ϕ)≤ f(E(G)).
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