Spectral radius, fractional [a,b][a,b]-factor and ID-factor-critical graphs

Let $G$ be a graph and $h: E(G)\rightarrow [0,1]$ be a function. For any two positive integers $a$ and $b$ with $a\leq b$, a fractional $[a,b]$-factor of $G$ with the indicator function $h$ is a spanning subgraph with vertex set $V(G)$ and edge set $E_h$ such that $a\leq\sum_{e\in E_{G}(v)}h(e)\leq b$ for any vertex $v\in V(G)$, where $E_h = \{e\in E(G)|h(e)>0\}$ and E_{G}(v)=\{e\in E(G)| e~\mbox{is incident with}~v~\mbox{in}~G\}. A graph $G$ is ID-factor-critical if for every independent set $I$ of $G$ whose size has the same parity as $|V(G)|$, $G-I$ has a perfect matching. In this paper, we present a tight sufficient condition based on the spectral radius for a graph to contain a fractional $[a,b]$-factor, which extends the result of Wei and Zhang [Discrete Math. 346 (2023) 113269]. Furthermore, we also prove a tight sufficient condition in terms of the spectral radius for a graph with minimum degree $\delta$ to be ID-factor-critical.Comment: 14 pages, 2 figure

Spectral radius and spanning trees of graphs

For integer $k\geq2,$ a spanning $k$-ended-tree is a spanning tree with at most $k$ leaves. Motivated by the closure theorem of Broersma and Tuinstra [Independence trees and Hamilton cycles, J. Graph Theory 29 (1998) 227--237], we provide tight spectral conditions to guarantee the existence of a spanning $k$-ended-tree in a connected graph of order $n$ with extremal graphs being characterized. Moreover, by adopting Kaneko's theorem [Spanning trees with constraints on the leaf degree, Discrete Appl. Math. 115 (2001) 73--76], we also present tight spectral conditions for the existence of a spanning tree with leaf degree at most $k$ in a connected graph of order $n$ with extremal graphs being determined, where $k\geq1$ is an integer

An improvement of sufficient condition for kk-leaf-connected graphs

For integer $k\geq2,$ a graph $G$ is called $k$-leaf-connected if $|V(G)|\geq k+1$ and given any subset $S\subseteq V(G)$ with $|S|=k,$ $G$ always has a spanning tree $T$ such that $S$ is precisely the set of leaves of $T.$ Thus a graph is $2$-leaf-connected if and only if it is Hamilton-connected. In this paper, we present a best possible condition based upon the size to guarantee a graph to be $k$-leaf-connected, which not only improves the results of Gurgel and Wakabayashi [On $k$-leaf-connected graphs, J. Combin. Theory Ser. B 41 (1986) 1-16] and Ao, Liu, Yuan and Li [Improved sufficient conditions for $k$-leaf-connected graphs, Discrete Appl. Math. 314 (2022) 17-30], but also extends the result of Xu, Zhai and Wang [An improvement of spectral conditions for Hamilton-connected graphs, Linear Multilinear Algebra, 2021]. Our key approach is showing that an $(n+k-1)$-closed non-$k$-leaf-connected graph must contain a large clique if its size is large enough. As applications, sufficient conditions for a graph to be $k$-leaf-connected in terms of the (signless Laplacian) spectral radius of $G$ or its complement are also presented.Comment: 15 pages, 2 figure

Identification of a novel strain of human papillomavirus from children with diarrhea in China

A highly divergent human papillomavirus (HPV) strain, HPV-L55, was identified in fecal samples from children hospitalized with diarrhea in China. The L1 gene of HPV-L55 shares <75% identity with previously reported HPVs, indicating that this virus represents a novel type of HPV. Phylogenetic analysis classified this virus as a member of the gammapapillomaviruses

Recovery of Salmonella isolated from eggs and the commercial layer farms

Abstract Background Salmonella is recognized as a common bacterial cause of foodborne diarrheal illness worldwide, and animal or its food products have been the most common vehicles of the Salmonella infections. This study aimed to investigate the distribution of Salmonella in two commercial layer farms and to determine the genetic relatedness between these strains. The Salmonella isolates were serotyped by slide agglutination using commercial antisera and analyzed for genetic relatedness using pulsed-field gel electrophoresis (PFGE). Results The internal environment had the highest prevalence of Salmonella (14/15, 93.3%), followed by external environment (60/96, 62.5%) and egg samples (23/84, 27.3%). The prevalence of Salmonella in the environment was significantly higher than that in egg samples (p < 0.05). The occurrence of Salmonella in the internal environment (93.3%) was relatively higher than in the external environment (55.6–77.2%). The 111 isolates were distributed among 15 PFGE types, and the PFGE results suggested that there existed cross-contamination between these strains not only from eggs, but also from the environments. Conclusions The findings indicated ongoing Salmonella cross-contamination inside or outside of the layer farms, and that Salmonella could also spread along the egg production line

MOESM1 of Recovery of Salmonella isolated from eggs and the commercial layer farms

Additional file 1: Table S1. The prevalence and distribution of Salmonella in egg samples

MOESM2 of Recovery of Salmonella isolated from eggs and the commercial layer farms

Additional file 2: Table S2. PEGE type of Salmonella in different origins of the two layer farms