A graph G is loosely-c-connected, or l-c-connected, if there exists a number d depending on G such that the deletion of fewer than c vertices from G leaves precisely one infinite component and a graph containing at most d vertices. In this paper, we give the structure of a set of l-c-connected infinite graphs that form an unavoidable set among the topological minors of l-c-connected infinite gr...

The Pósa-Seymour conjecture asserts that every graph on n vertices with minimum degree at least (1−1/(r +1))n contains the r-th power of a Hamilton cycle. Komlós, Sárközy and Szemerédi famously proved for large n. notion discrepancy appears in many areas mathematics, including theory. In this setting, G is given along 2-coloring its edges. One then asked to find copy subgraph discrepancy, i.e.,...

Robotic 3D bin packing (R-3dBPP), aiming to place deformed cases in various sizes the container without fences, is a comprehensive application that includes perception, planning, execution, and hardware design. Traditional studies assume context of real space must be accurately perceived represented. However, disjunctions between planner reality are unavoidable R-3dBPP, especially with low-cost...