Thomas Dale Porter

On a bottleneck bipartition conjecture of Erdös

AbstractFor a graphG, let γ(U,V)=max{e(U), e(V)} for a bipartition (U, V) ofV(G) withUυV=V(G),UφV=Ø. Define γ(G)=min(U,V){γ(U,V)}. Paul Erdős conjectures

A hierarchy of self-clique graphs

\gamma (G)/e(G) \leqslant {1 \mathord{\left/ {\vphantom {1 4}} \right. \kern-\nulldelimiterspace} 4} + O\left( {1/\sqrt {e(G)} } \right)

SELF-CLIQUE GRAPHS WITH PRESCRIBED CLIQUE-SIZES

. This paper verifies the conjecture and shows

Closed-Neighborhood Anti-Sperner Graphs

\gamma (G)/e(G) \leqslant {1 \mathord{\left/ {\vphantom {1 4}} \right. \kern-\nulldelimiterspace} 4}\left( {1 + \sqrt {2/e(G)} } \right)

Binomial Identities Generated by Counting Spanning Trees.

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ENUMERATING LABELLED GRAPHS WITH CERTAIN NEIGHBORHOOD PROPERTIES

Abstract Let { G p 1 , G p 2 , … } be an infinite sequence of graphs with G pn having pn vertices. This sequence is called K p -removable if G p 1 ≅ K p , and G pn - S ≅ G p ( n - 1 ) for every n ⩾ 2 and every vertex subset S of G pn that induces a K p . Each graph in such a sequence has a high degree of symmetry: every way of removing the vertices of any fixed number of disjoint K p s yields the same subgraph. Here we construct such sequences using componentwise Eulerian digraphs as generators. The case in which each G pn is regular is also studied, where Cayley digraphs based on a finite group are used.