Abstract Bipartite incidence graph sampling provides a unified representation of many situations for the purpose estimation, including existing unconventional methods, such as indirect, network or adaptive cluster sampling, which are not originally described problems. We develop large class design-based linear estimators, defined sample edges and subjected to general condition design unbiasedne...

For a graph G , we define the lower bipartite number LB( ) as minimum order of maximal induced subgraph . We study parameter, and related parameter domination, providing bounds both in general graphs some families. example, show that there are arbitrarily large 4-connected planar with = 4 but 5-connected has linear ). also if is outerplanar n then lies between ( + 2)/3 2 /3, these sharp.

A graph is connected-homogeneous if any isomorphism between finite connected induced subgraphs extends to an automorphism of the graph. In this paper we classify the countably infinite connectedhomogeneous graphs. We prove that if Γ is connected countably infinite and connected-homogeneous then Γ is isomorphic to one of: Lachlan and Woodrow’s ultrahomogeneous graphs; the generic bipartite graph...

For a 3-colourable graph G, the 3-colour graph of G, denoted C3(G), is the graph with node set the proper vertex 3-colourings of G, and two nodes adjacent whenever the corresponding colourings differ on precisely one vertex of G. We consider the following question : given G, how easily can we decide whether or not C3(G) is connected? We show that the 3-colour graph of a 3-chromatic graph is nev...

An edge-coloring of a graph G with colors 1, . . . , t is an interval t-coloring if all colors are used, and the colors of edges incident to each vertex of G are distinct and form an interval of integers. A graph G is interval colorable if it has an interval t-coloring for some positive integer t. The problem of deciding whether a bipartite graph is interval colorable is NP-complete. The smalle...