论文标题
双子曲霉的双回路
Double circuits in bicircular matroids
论文作者
论文摘要
哈德威格（Hadwiger）针对定向的矩阵的猜想的第一个非平凡案例如下所示。如果$ \ MATHCAL {O} $是$ M（K_4）$ - 免费定向的Matroid，则$ \ Mathcal {O} $接纳A NZ $ 3 $ -COFLOW，即在Hochstättler-nešetmennešet月中，它是$ 3 $ -COLOURABLE。 γ类是$ m（k_4）$的类别 - 免费定向的矩阵，是最小的次要闭合类，其中包含所有横向矩阵。为了证明先前关于γ类，Goddyn，Hochstättler和Neudauer的陈述，指出每个伽马体都有阳性的coline（等效地，是一个正双回路），这意味着γ-所有方向均为$ 3 $ 3美元。在此简短的说明中，我们通过展示一大群不包含正双重电路的双圆形矩阵，反驳了Goddyn，Hochstättler和Neudauers的猜想。
The first non-trivial case of Hadwiger's conjecture for oriented matroids reads as follows. If $\mathcal{O}$ is an $M(K_4)$-free oriented matroid, then $\mathcal{O}$ admits a NZ $3$-coflow, i.e., it is $3$-colourable in the sense of Hochstättler-Nešetřil. The class of gammoids is a class of $M(K_4)$-free orientable matroids and it is the minimal minor-closed class that contains all transversal matroids. Towards proving the previous statement for the class of gammoids, Goddyn, Hochstättler, and Neudauer conjectured that every gammoid has a positive coline (equivalently, a positive double circuit), which implies that all orientations of gammoids are $3$-colourable. In this brief note we disprove Goddyn, Hochstättler, and Neudauers' conjecture by exhibiting a large class of bicircular matroids that do not contain positive double circuits.
