An ordered Ruzsa-Szemeredi graph is a graph whose edge set is partitioned into equal-size matchings, each induced in the suffix of the ordering that begins with it. Behnezhad and Ghafari introduced them to parametrize the update time of fully dynamic matching, but almost nothing is known about the numbers themselves. Writing f(n) for the largest number of parts when the matchings have size two, we determine f(n) exactly for every order from five to nineteen, narrow order twenty to two consecutive values, and give an explicit asymptotic construction. The engine is a bijection between ordered decompositions and K_4-peelings of the complete graph, each step deleting a perfect matching from four vertices that currently span a clique. This yields the counting bound floor(n(n-4)/4) at once and reduces equality to whether a cubic or near-cubic remainder is reachable. Structural lemmas cut the candidates to connected bridgeless graphs, and a contraction correspondence carries odd orders to the even census one larger, leaving a finite case analysis that we discharge by isomorphism-free reverse search. The bound is attained only at orders five through nine and eleven, and missed by exactly one at every other order we reach. Order eleven is thus an isolated exception rather than a parity phenomenon: the natural equality conjecture fails, and fails irregularly. Upper bounds are certified by fail-closed sweeps over complete cubic censuses, and every decomposition is re-checked against the definition by an independent verifier. Which of its two values order twenty takes remains open.
INTRODUCTION
Characterized as an idiopathic primary myocardial disorder, dilated cardiomyopathy (DCM) predominantly affects children and elderly adults. However, a lack of specific clinical symptoms and reliable biomarkers impedes timely diagnosis and rational clinical management of DCM.
METHODS
Whole-genome expression profiles (GSE120895, GSE9800) were retrieved from the Gene Expression Omnibus database via the GEOquery R package. A series of bioinformatic methods were employed, including DEG, GSVA, WGCNA, GO/KEGG enrichment, PPI, and immune infiltration analysis. Key biomarkers were validated by qRT-PCR in a Doxorubicin (DOX)-induced DCM model.
RESULTS
In total, 629 differentially expressed genes (DEGs) were screened out between DCM and control groups. Combined analysis of DEGs and WGCNA outputs identified 13 hub genes overlapping with oxidative stress-associated gene modules. Receiver Operating Characteristic (ROC) curve analyses confirmed that these hub genes exhibit favorable diagnostic efficiency for DCM. Functional enrichment results showed that these genes are mainly enriched in transmembrane transport and nucleotide metabolism pathways. Immune infiltration analysis indicated significantly elevated infiltration levels of five immune cell subsets in DCM myocardial tissues. In vivo experiments verified the significant upregulation of five core hub genes in DOX-induced DCM mice. By screening hub genes with diagnostic potency based on public transcriptome datasets and validating their expression alterations in a DOX-induced DCM animal model, this study provides partial experimental evidence to support the above bioinformatic outcomes.
DISCUSSION
Through integrative analysis of multiple datasets and molecular biology validation, this study provides robust evidence supporting the involvement of these hub genes in DCM pathogenesis. Although validation was limited to a single murine model, the findings lay the groundwork for future mechanistic studies and clinical exploration of these candidate genes.
CONCLUSION
Hub genes including MVP, WISP1, FCN1, AMPD3, RARRES1, FTL, and KRT14 possess promising auxiliary diagnostic potential, which provides novel clues for subsequent clinical evaluation research on DCM.