Cichacz–Suchan conjecture on irregular minimum k-critical-bipartite graphs

Let $n,m$ be positive integers such that $n>m>1$, let $k=n-m$, and set $a=\frac{m(k+1)}{n}$, which is not an integer. For the bipartite graph $\widehat{G}_{n,m}^{\lceil a\rceil}$ constructed with

$$U=\{u_i\mid i\in[n]\},\qquad V=\{v_j\mid j\in[m]\},$$

and

$$E=\left\{(u_i,v_{(j+\alpha)\bmod m})\mid i\in[n],\ \alpha\in[\lceil a\rceil],\ j=\left\lceil\frac{im}{n}\right\rceil\right\},$$

Cichacz–Suchan's conjecture. The graph $\widehat{G}_{n,m}^{\lceil a\rceil}$ is $k$-critical-bipartite. This means that after the removal of any $k$ vertices from $U$, every vertex in $V$ can still be matched to a distinct remaining vertex in $U$. The conjecture extends the corresponding result for the case in which $a=\frac{m(k+1)}{n}$ is an integer to the irregular case.