Berge，Fulkerson and Seymour的作品
Bricks and conjectures of Berge, Fulkerson and Seymour
摘要：
一个$r$ -图是一个$r$ -正则图，其中每个奇数顶点集至少通过$r$边连接到图的其余部分。Seymour证明了任何$r$ -图都是$r+1$ -边可着色的，并且任何$r$ -图都包含$2r$完美匹配，使得每条边属于其中的两条。我们表明，最小的反例，这些结构是一块砖。此外，我们反证范，Raspaud猜想的一个变种。
英文摘要：
An $r$-graph is an $r$-regular graph where every odd set of vertices is connected by at least $r$ edges to the rest of the graph. Seymour conjectured that any $r$-graph is $r+1$-edge-colorable, and also that any $r$-graph contains $2r$ perfect matchings such that each edge belongs to two of them. We show that the minimum counter-example to either of these conjectures is a brick. Furthermore we disprove a variant of a conjecture of Fan, Raspaud.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
