We have 5 of 45 papers
We haven’t gathered this author’s papers yet. Follow them and we’ll fetch their work.
Not the right person? Other researchers publish under this name.
Tutte's flow conjectures ask when a graph has a nowhere-zero flow with small integer values. We approach these questions through spanning-tree packing and an analytic minimization argument of Alon, Buci\'c, and Davies. For every integer $q\ge2$, we prove that $q$ edge-disjoint spanning trees suffice to realize every co...
The List Edge-Coloring Conjecture predicts that any graph whose edges can be colored with $k$ colors can also be colored from arbitrary lists of $k$ colors. We prove its stronger online form for two new infinite families, $K_{p-1}$ and $K_{2p}$, where $p$ is an odd prime. For even $n$, order the vertices of $K_n$ and d...
Let $q=p^k$, and let $A_1,\ldots,A_{r-1}$ be invertible $n\times n$ matrices over ${\mathbb F}_q$. We prove that, if $k\ge r$, there is a vector $x$ for which \[ x,A_1x,\ldots,A_{r-1}x \] are all nowhere zero. For $r=2$ this recovers the theorem of Alon and Tarsi over nonprime finite fields. The proof tracks one monomi...
Fix positive integers $N,k,n$ with $n\ge k$. We seek the minimum number of members of size at least $n$ in a finite family of finite sets closed under union and containing exactly $N$ distinct sets of size $k$. This problem is a specialization of the Leck--Roberts--Simpson weighted conjecture: assign weight one to sets...
Let $q=p^k$, where $p$ is prime, and let $M$ be a finite matroid representable over ${\Bbb{F}}_q$. Write $\chi_M(t)$ for its characteristic polynomial and $\mbox{decop}(M)$ for the least number of independent sets needed to cover its ground set. We prove that $\chi_M(q)>0$ whenever $k\ge\mbox{decop}(M)$. Geometrically,...
We use cookies to run the site and, with your consent, for analytics and to show ads. See our Cookie Policy.
