منابع مشابه
Between 2- and 3-Colorability
We consider the question of the existence of homomorphisms between Gn,p and odd cycles when p = c/n, 1 < c ≤ 4. We show that for any positive integer l, there exists ε = ε(l) such that if c = 1 + ε then w.h.p. Gn,p has a homomorphism from Gn,p to C2l+1 so long as its odd-girth is at least 2l+1. On the other hand, we show that if c = 4 then w.h.p. there is no homomorphism from Gn,p to C5. Note t...
متن کامل3-Colorability of Pseudo-Triangulations
Deciding 3-colorability for general plane graphs is known to be an NP-complete problem. However, for certain classes of plane graphs, like triangulations, polynomial time algorithms exist. We consider the family of pseudo-triangulations (a generalization of triangulations) and prove NP-completeness for this class. The complexity status does not change if the maximum face-degree is bounded to fo...
متن کاملVertex 3-colorability of Claw-free Graphs
The 3-colorability problem is NP-complete in the class of clawfree graphs and it remains hard in many of its subclasses obtained by forbidding additional subgraphs. (Line graphs and claw-free graphs of vertex degree at most four provide two examples.) In this paper we study the computational complexity of the 3-colorability problem in subclasses of claw-free graphs defined by finitely many forb...
متن کاملLow Degree Nullstellensatz Certificates for 3-Colorability
In a seminal paper, De Loera et. al introduce the algorithm NulLA (Nullstellensatz Linear Algebra) and use it to measure the difficulty of determining if a graph is not 3-colorable. The crux of this relies on a correspondence between 3-colorings of a graph and solutions to a certain system of polynomial equations over a field k. In this article, we give a new direct combinatorial characterizati...
متن کاملOn the 2-Colorability of Random Hypergraphs
A 2-coloring of a hypergraph is a mapping from its vertices to a set of two colors such that no edge is monochromatic. Let Hk(n,m) be a random k-uniform hypergraph on n vertices formed by picking m edges uniformly, independently and with replacement. It is easy to show that if r ≥ rc = 2k−1 ln 2− (ln 2)/2, then with high probability Hk(n,m = rn) is not 2-colorable. We complement this observatio...
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ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 2015
ISSN: 1077-8926
DOI: 10.37236/4673