发表机构
Sichuan Normal University; Minnan Normal University（四川师范大学; 闽南师范大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究了近二部砖块中每个b-不变边都是强迫边的图，给出了完整刻画。
AI 中文摘要
如果一个连通图至少有一条边且每条边都属于某个完美匹配，则称其为匹配覆盖图。Lovász证明每个匹配覆盖图G可以唯一地分解为一系列砖块和 braces（多重边允许）。记b(G)为这种分解中砖块的数量。G的边e是可移除的，如果G-e仍然是匹配覆盖图；如果e是可移除且b(G-e)=b(G)，则称e是b-不变的。此外，G的边e是强迫边，如果它恰好属于G的一个完美匹配。Lucchesi和Murty提出了刻画不同于K_4、\overline{C_6}和Petersen图的砖块的问题，其中每个b-不变边都是强迫边。本文通过给出完整刻画，解决了近二部砖块的情形。
英文摘要
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 decomposed into a list of bricks and braces up to multiple edges. Denote by b(G) the number of bricks in such a decomposition. An edge e of G is removable if G-e is also matching covered; is b-invariant if e is removable and b(G-e)=b(G). Furthermore, an edge e of G is a forcing edge if it lies in precisely one perfect matching of G. Lucchesi and Murty proposed the problem of characterizing bricks, distinct from K_4, \overline{C_6}, and the Petersen graph, in which every b-invariant edge is a forcing edge. In this paper, we solve this problem for near-bipartite bricks by providing a complete characterization.
Comments15 pages, 9 figures
