A graph G of order 2n is called degree-equipartite if for every n-element set A ⊆ V (G), the degree sequences of the induced subgraphs G[A] and G[V (G) \ A] are the same. In this paper, we… (More)

A graph G of order 2n is called equipartite if for every n-element set A ⊆ V (G), there exists an automorphism of G that maps the induced subgraph G[A] onto G[V (G)\A]. In this paper, we show that a… (More)

The Erdős-Gyárfás conjecture states that every graph with minimum degree at least three has a cycle whose length is a power of 2. Since this conjecture has proven to be far from reach, Hobbs asked if… (More)