15 papers
UMAS3D: Unified Mask-Free 3D Editing with Region-Adaptive Source Preservation
Xianlin Zeng, Xiaolong Shen, Ruijie Quan +1
3D editing aims to modify an existing 3D asset according to user intent while preserving geometry and appearance outside the intended edit region. Existing methods often rely on ta…
Bricks that every removable edge is solitary
Jinxin Xue, Jun Ge, Fuliang Lu +1
A brick is a 3-connected graph such that has a perfect matching for any two distinct vertices . An edge in a matching covered graph is removable if…
Near-bipartite bricks in which every b-invariant edge is a forcing edge
Yaxian Zhang, Fuliang Lu
A connected graph is matching covered if it has at least one edge and every edge lies in some perfect matching.Lovász proved that every matching covered graph G can be uniquely dec…
Bricks in which every vertex is incident with a forcing edge
Xinyu Dai, Fuliang Lu, Yaxian Zhang
A matching covered graph is a brick if it is 3-connected and bicritical. An edge of a matching covered graph G is a forcing edge if it lies in precisely one perfect matching of G.…
Tight cuts in matching covered graphs
Fuliang Lu, Fengming Dong
An edge cut C of a graph G is tight if |C \M| = 1 for every perfect matching M of G. Barrier-cuts and 2-separation cuts, also referred to as ELP-cuts, are two important types of ti…
Adjacent vertices of small degree in minimal matching covered graphs
Xiaoling He, Fuliang Lu, Heping Zhang
A connected graph with at least two vertices is matching covered if each of its edges lies in a perfect matching. A matching covered graph is minimal if the removal of any edge…
On minimal k-factor-critical planar graphs
Qiuli Li, Fuliang Lu, Heping Zhang
A graph of order is said to be \emph{-factor-critical} () if the removal of any vertices results in a graph with a perfect matching. A -factor-critical gr…
The minimum degree of minimal 2-extendable claw-free graphs
Jing Guo, Fuliang Lu, Heping Zhang
A connected graph with a perfect matching is said to be -extendable for integers , , if any matching in of size is contained in a…
Wheel-like bricks and minimal matching covered graphs
Xiaoling He, Fuliang Lu, Jinxin Xue
A connected graph G with at least two vertices is matching covered if each of its edges lies in a perfect matching. We say that an edge e in a matching covered graph G is removable…
Cubic bricks that every b-invariant edge is forcing
Yaxian Zhang, Fuliang Lu, Heping Zhang
A connected graph G is matching covered if every edge lies in some perfect matching of G. Lovasz proved that every matching covered graph G can be uniquely decomposed into a list o…
Planar wheel-like bricks
Fuliang Lu, Jinxin Xue
An edge e in a matching covered graph G is removable if G-e is matching covered; a pair {e; f} of edges of G is a removable doubleton if G-e-f is matching covered, but neither G-e…
The number of perfect matchings in a brick
Fuliang Lu, Huali Pan
A 3-connected graph is a brick if the graph obtained from it by deleting any two distinct vertices has a perfect matching. The importance of bricks stems from the fact that they ar…
Removable edges in near-bipartite bricks
Yipei Zhang, Fuliang Lu, Xiumei Wang +1
An edge of a matching covered graph is removable if is also matching covered. The notion of removable edge arises in connection with ear decompositions of matching co…
The minimum degree of minimal -factor-critical claw-free graphs*
Jing Guo, Qiuli Li, Fuliang Lu +1
A graph of order is said to be -factor-critical for integers , if the removal of any vertices results in a graph with a perfect matching. A -factor-cr…
Removable edges in cubic matching covered graphs
Lu Fuliang, Qian Jianguo
{ An edge in a matching covered graph is {\em removable} if is matching covered, which was introduced by Lovász and Plummer in connection with ear decompositions of m…