ترغب بنشر مسار تعليمي؟ اضغط هنا

A Proof of a Conjecture of Ohba

136   0   0.0 ( 0 )
 نشر من قبل Jonathan Noel
 تاريخ النشر 2012
  مجال البحث الهندسة المعلوماتية
والبحث باللغة English




اسأل ChatGPT حول البحث

We prove a conjecture of Ohba which says that every graph $G$ on at most $2chi(G)+1$ vertices satisfies $chi_ell(G)=chi(G)$.

قيم البحث

اقرأ أيضاً

A typical decomposition question asks whether the edges of some graph $G$ can be partitioned into disjoint copies of another graph $H$. One of the oldest and best known conjectures in this area, posed by Ringel in 1963, concerns the decomposition of complete graphs into edge-disjoint copies of a tree. It says that any tree with $n$ edges packs $2n+1$ times into the complete graph $K_{2n+1}$. In this paper, we prove this conjecture for large $n$.
We give a new proof of a sumset conjecture of Furstenberg that was first proved by Hochman and Shmerkin in 2012: if $log r / log s$ is irrational and $X$ and $Y$ are $times r$- and $times s$-invariant subsets of $[0,1]$, respectively, then $dim_text{ H} (X+Y) = min ( 1, dim_text{H} X + dim_text{H} Y)$. Our main result yields information on the size of the sumset $lambda X + eta Y$ uniformly across a compact set of parameters at fixed scales. The proof is combinatorial and avoids the machinery of local entropy averages and CP-processes, relying instead on a quantitative, discrete Marstrand projection theorem and a subtree regularity theorem that may be of independent interest.
86 - Marino Romero 2020
In the context of the (generalized) Delta Conjecture and its compositional form, DAdderio, Iraci, and Wyngaerd recently stated a conjecture relating two symmetric function operators, $D_k$ and $Theta_k$. We prove this Theta Operator Conjecture, findi ng it as a consequence of the five-term relation of Mellit and Garsia. As a result, we find surprising ways of writing the $D_k$ operators.
Motivated by a hat guessing problem proposed by Iwasawa cite{Iwasawa10}, Butler and Graham cite{Butler11} made the following conjecture on the existence of certain way of marking the {em coordinate lines} in $[k]^n$: there exists a way to mark one po int on each {em coordinate line} in $[k]^n$, so that every point in $[k]^n$ is marked exactly $a$ or $b$ times as long as the parameters $(a,b,n,k)$ satisfies that there are non-negative integers $s$ and $t$ such that $s+t = k^n$ and $as+bt = nk^{n-1}$. In this paper we prove this conjecture for any prime number $k$. Moreover, we prove the conjecture for the case when $a=0$ for general $k$.
We prove that for any $varepsilon>0$, for any large enough $t$, there is a graph $G$ that admits no $K_t$-minor but admits a $(frac32-varepsilon)t$-colouring that is frozen with respect to Kempe changes, i.e. any two colour classes induce a connected component. This disproves three conjectures of Las Vergnas and Meyniel from 1981.
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا