H-minimal Graphs of Low Regularity in H1

Obstructions to the Existence of Smooth Solutions to the Plateau Problem in H1

In this paper we investigate H-minimal graphs of lower regularity. We show that noncharactersitic C H-minimal graphs are ruled surfaces with C seed curves. Moreover, in light of a structure theorem of Franchi, Serapioni and Serra Cassano, we see that any H-minimal surface is, up to a set of perimeter zero, composed of such pieces. Along these lines, we investigate ways in which patches of C H-m...

H - Minimal Graphs of Low Regularity

In this paper we investigate H-minimal graphs of lower regularity. We show that noncharactersitic C H-minimal graphs are ruled surfaces with C seed curves. Moreover, in light of a structure theorem of Franchi, Serapioni and Serra Cassano, we see that any H-minimal surface is, up to a set of perimeter zero, composed of such pieces. Along these lines, we investigate ways in which patches of C H-m...

All Ramsey (2K2,C4)−Minimal Graphs

Let F, G and H be non-empty graphs. The notation F → (G,H) means that if any edge of F is colored by red or blue, then either the red subgraph of F con- tains a graph G or the blue subgraph of F contains a graph H. A graph F (without isolated vertices) is called a Ramsey (G,H)−minimal if F → (G,H) and for every e ∈ E(F), (F − e) 9 (G,H). The set of all Ramsey (G,H)−minimal graphs is denoted by ...

Mixed cycle-E-super magic decomposition of complete bipartite graphs

An H-magic labeling in a H-decomposable graph G is a bijection f : V (G) ∪ E(G) → {1, 2, ..., p + q} such that for every copy H in the decomposition, ΣνεV(H) f(v) +  ΣeεE(H) f(e) is constant. f is said to be H-E-super magic if f(E(G)) = {1, 2, · · · , q}. A family of subgraphs H1,H2, · · · ,Hh of G is a mixed cycle-decomposition of G if every subgraph Hi is isomorphic to some cycle Ck, for k ≥ ...

Bounds for the Regularity of Edge Ideal of Vertex Decomposable and Shellable Graphs