California State University (CSU): Open Journal Systems
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A Proof Using Böhme\u27s Lemma That no Petersen Family Graph has a Flat Embedding
No full textSachs and Conway-Gordon used linking number and a beautiful counting argument to prove that every graph in the Petersen family is intrinsically linked (have a pair of disjoint cycles that form a nonsplit link in every spatial embedding) and thus each family member has no flat spatial embedding (an embedding for which every cycle bounds a disk with interior disjoint from the graph). We give an alternate proof that every Petersen family graph has no flat embedding by applying Böhme\u27s Lemma and the Jordan-Brouwer Separation Theorem
Always Wondering Always Trying
Get PDFZhijiao Yang, a postgraduate accounting student at Durham University, diligently seeks her life’s direction as a first-generation college student. In this essay, Zhijiao narrates her journey, reflecting on her childhood as a left-behind child and the profound impact of her parents’ support on her education. The narrative highlights the resilience, open-mindedness, and self-reliance she has developed, and offers advice to fellow first-gen students on embracing challenges and navigating uncertainties
