1 1 O ct 2 01 1 Disproof of the List Hadwiger Conjecture
نویسندگان
چکیده
The List Hadwiger Conjecture asserts that every Kt-minor-free graph is t-choosable. We disprove this conjecture by constructing a K3t+2-minor-free graph that is not 4tchoosable for every integer t ≥ 1.
منابع مشابه
Disproof of the List Hadwiger Conjecture
The List Hadwiger Conjecture asserts that every Kt-minor-free graph is tchoosable. We disprove this conjecture by constructing a K3t+2-minor-free graph that is not 4t-choosable for every integer t ≥ 1.
متن کاملNormality of the Ehrenfeucht-Mycielski Sequence
We study the binary Ehrenfeucht Mycielski sequence seeking a balance between the number of occurrences of different binary strings. There have been numerous attempts to prove the balance conjecture of the sequence, which roughly states that 1 and 0 occur equally often in it. Our contribution is twofold. First, we study weaker forms of the conjecture proved in the past and lay out detailed proof...
متن کاملContractibility and the Hadwiger Conjecture
Consider the following relaxation of the Hadwiger Conjecture: For each t there exists Nt such that every graph with no Kt minor admits a vertex partition into dαt + βe parts, such that each component of the subgraph induced by each part has at most Nt vertices. The Hadwiger Conjecture corresponds to the case α = 1, β = −1 and Nt = 1. Kawarabayashi and Mohar [K. Kawarabayashi, B. Mohar, A relaxe...
متن کاملDisproof of the Mertens Conjecture
The Mertens conjecture states that M(x) < x ⁄2 for all x > 1, where M(x) = n ≤ x Σ μ(n) , and μ(n) is the Mo bius function. This conjecture has attracted a substantial amount of interest in its almost 100 years of existence because its truth was known to imply the truth of the Riemann hypothesis. This paper disproves the Mertens conjecture by showing that x → ∞ lim sup M(x) x − ⁄2 > 1. 06 ....
متن کاملOn Set Systems with Restricted Intersections Modulo a Composite Number
Let S be a set of n elements, and let H be a set-system on S, which satisses that the size of any element of H is divisible by m, but the intersection of any two elements of H is not divisible by m. If m is a prime or prime-power, then the famous Frankl{Wilson theorem 3] implies that jHj = O(n m?1), i.e. for xed m, its size is at most polynomial in n. This theorem has numerous applications in c...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2011