In this paper, we discuss a pair of chromatically equivalent of K4-homeomorphs of girth 11, that is, K4(1, 3, 7, d, e, f) and K4(1, 3, 7, d′, e′, f ′). As a result, we obtain two infinite chromatically equivalent non-isomorphic K4-homeomorphs. Mathematical Subject Classification: 05C15

Let P be the Petersen graph. The main results of this paper are the discovery of infinite families of chromatically equivalent pairs of P homeomorphs and the discovery of infinite families of flow equivalent pairs of P amallamorphs. In particular, three families of P homeomorphs with 8 parameters, five families with 7 parameters and many families with fewer parameters are obtained. Also one fam...

In this paper, we study the chromatic uniqueness of one family of K4-homeomorphs with girth 10. 2000 Mathematical Subject Classification. Primary 05C15.

In this paper, we study the chromatic uniqueness of one family of K4-homeomorphs with girth 10. 2000 Mathematics Subject Classification: 05C15

We prove a uniform bound on the topological Turán number of an arbitrary two-dimensional simplicial complex S: any n vertices with at least CSn3−1/5 facets contains homeomorph S, where CS > 0 is constant depending S alone. This result, analogue classical one-dimensonal result Mader, sheds some light old problem Linial from 2006.

A K4-homeomorph is a subdivision of the complete graph with four vertices (K4). Such a homeomorph is denoted by K4(a,b,c,d,e,f) if the six edges of K4 are replaced by the six paths of length a,b,c,d,e,f, respectively. In this paper, we discuss the chromaticity of a family of K4-homeomorphs with girth 10. We also give sufficient and necessary condition for some graphs in the family to be chromat...