A Computer-Assisted Proof of the Barnette--Goodey Conjecture: Not Only Fullerene Graphs Are Hamiltonian

the impact of computer-assisted language learning on achievement motivation of high school students

چکیده انگیزه دلیل اصلی رفتارهای ما است. به نظر می رسد انگیزه جزء جدایی ناپذیر فرایند یادگیری باشد. ارزش ذاتی موفقیت تمایل به پیشرفت را در یادگیرنده ایجاد میکند. به عبارت ساده این تمایل انگیزه پیشرفت نامیده میشود. انگیزه پیشرفت را میتوان در احساس یادگیرنده هنگام چالش با درس های مدرسه، لذت انجام فعالیت درسی، یا حس کشف پاسخ مشاهده کرد.حتی ممکن است انگیزه پیشرفت را در تلاش یادگیرنده برای جلب تایید...

Hamiltonian chordal graphs are not cycle extendible

In 1990, Hendry conjectured that every Hamiltonian chordal graph is cycle extendible; that is, the vertices of any non-Hamiltonian cycle are contained in a cycle of length one greater. We disprove this conjecture by constructing counterexamples on n vertices for any n ≥ 15. Furthermore, we show that there exist counterexamples where the ratio of the length of a non-extendible cycle to the total...

Proof of a conjecture on monomial graphs

Let e be a positive integer, p be an odd prime, q = p, and Fq be the finite field of q elements. Let f, g ∈ Fq[X,Y ]. The graph G = Gq(f, g) is a bipartite graph with vertex partitions P = F3q and L = F 3 q, and edges defined as follows: a vertex (p) = (p1, p2, p3) ∈ P is adjacent to a vertex [l] = [l1, l2, l3] ∈ L if and only if p2 + l2 = f(p1, l1) and p3 + l3 = g(p1, l1). Motivated by some qu...

A Computer-assisted Proof of Saari’s Conjecture for the Planar Three-body Problem

The five relative equilibria of the three-body problem give rise to solutions where the bodies rotate rigidly around their center of mass. For these solutions, the moment of inertia of the bodies with respect to the center of mass is clearly constant. Saari conjectured that these rigid motions are the only solutions with constant moment of inertia. This result will be proved here for the planar...

Oriented Hamiltonian Paths in Tournaments: A Proof of Rosenfeld's Conjecture