Vertices with the Second Neighborhood Property in Eulerian Digraphs

The Second Neighborhood Conjecture states that every simple digraph has a vertex whose second out-neighborhood is at least as large as its first out-neighborhood, i.e. a vertex with the Second Neighborhood Property. A cycle intersection graph of an even graph is a new graph whose vertices are the cycles in a cycle decomposition of the original graph and whose edges represent vertex intersections of the cycles. By using a digraph variant of this concept, we prove that Eulerian digraphs which admit a simple dicycle intersection graph have not only adhere to the Second Neighborhood Conjecture, but have a vertex of minimum outdegree that has the Second Neighborhood Property.Comment: fixed an error in an earlier version and made structural change

MYC Expression in Concert with BCL2 and BCL6 Expression Predicts Outcome in Chinese Patients with Diffuse Large B-Cell Lymphoma, Not Otherwise Specified

<div><p>Recent studies provide convincing evidence that a combined immunohistochemical or fluorescence <i>in situ</i> hybridization (FISH) score of MYC, BCL2, BCL6 proteins and <i>MYC</i> translocations predicted outcome in diffuse large B-cell lymphoma (DLBCL) patients treated with rituximab, cyclophosphamide, doxorubicin, vincristine, and prednisone (R-CHOP). However, by far, all these researches are based on Western populations. Therefore, we investigate the prognostic relevance of MYC-, BCL2- and BCL6-rearrangements and protein expression by immunohistochemistry and FISH from 336 <i>de novo</i> DLBCL, NOS treated with CHOP or R-CHOP. Breaks in <i>MYC</i> and <i>BCL6</i>, and fusion in <i>IGH/BCL2</i> were detected in 9.7%, 20.0%, and 11.1% of the cases, respectively, and were not significantly associated with clinical outcomes. Protein overexpression of MYC (≥40%), BCL2 (≥70%) and BCL6 (≥50%) was encountered in 51%, 51% and 36% of the tumors, respectively. On the basis of MYC, BCL2 and BCL6 expression, double-hit scores (DHSs) and triple-hit score (THS) were assigned to all patients with DLBCL. Patients with high MYC/BCL2 DHS, high MYC/BCL6 DHS and high THS had multiple adverse prognostic factors including high LDH level, poor performance status, advanced clinical stage, high International Prognostic Index (IPI) score, and non-germinal center B-cell. In univariate analysis, high MYC/BCL2 DHS, high MYC/BCL6 DHS and high THS were associated with inferior OS and PFS in both CHOP and R-CHOP cohorts (<i>P</i><0.05). The highly significant correlations with OS and PFS were maintained in multivariate models that controlled for IPI (<i>P</i><0.05). DLBCLs with high DHSs and high THS share the clinical features and poor prognosis of double-hit lymphoma (<i>P</i>>0.05). These data together suggest that the immunohistochemical DHSs and THS defined a large subset of DLBCLs with double-hit biology and was strongly associated with poor outcome in patients treated with R-CHOP or CHOP.</p></div

Prognostic impact of immunohistochemical subtypes in DLBCL risk-stratified according to treatments.

<p>(A, B) OS (A) and PFS (B) of all patients with GCB subtype or non-GCB subtype. (C, D) OS (C) and PFS (D) of CHOP-treated patients with GCB subtype or non-GCB subtype. (E, F) OS (E) and PFS (F) of R-CHOP-treated patients with GCB subtype or non-GCB subtype. OS, overall survival; PFS, progression-free survival; GCB, germinal center B-cell.</p

Prognostic impact of MYC, BCL2, BCL6 and Ki67 expression in DLBCL patients treated with CHOP.

<p>Patients’ tumors were stained for (A, B) MYC, (C, D) BCL2, (E, F) BCL6, and (G, H) Ki67. The numbers of patients showing negative or positive stainings (MYC≥40%, BCL2≥70%, BCL6≥50%, Ki67≥90%), cut-off values, and <i>P</i> values are indicated.</p

Multivariate Cox models for DBCL, NOS patients treated with CHOP (n = 203).

<p>Bold font indicates significance.</p><p>*Cox regression enter method.</p

Prognostic impact of treatments in DLBCL risk-stratified according to immunohistochemical subgroups.

<p>(A, B) OS (A) and PFS (B) of all patients treated with CHOP or R-CHOP. (C, D) OS (C) and PFS (D) of patients treated with CHOP or R-CHOP in GCB subgroup. (E, F) OS (E) and PFS (F) of patients treated with CHOP or R-CHOP in non-GCB subgroup. OS, overall survival; PFS, progression-free survival; GCB, germinal center B-cell.</p

Univariate Cox models for DLBCL, NOS patients treated with R-CHOP.

<p>Bold font indicates significance.</p>#<p>Sample sizes differ due to complete data set per cox model.</p

Patient clinical and immunophenotypical characteristics of patients with DLBCL, NOS in relation to DHS and THS.

<p><i>P</i> values were derived using Pearson’s Chi-Square test. Bold font indicates significance.</p><p>*NS, not suitable for chi-square test among CD5+ <i>vs.</i> GCB <i>vs.</i> non-GCB, because more than 1/5 of the expected values were less than five.</p>#<p><i>P</i> value GCB <i>vs.</i> non-GCB.</p

Patient clinical and immunophenotypical characteristics of patients with DLBCL, NOS in relation to protein expressions.

<p><i>P</i> values were derived from Pearson’s Chi-Square test. Bold font indicates significance. ULN, upper limit of normal.</p><p>*<i>P</i> value CD5+ <i>vs.</i> GCB <i>vs.</i> non-GCB.</p>#<p><i>P</i> value GCB <i>vs.</i> non-GCB.</p

Prognostic impact of MYC, BCL2, BCL6 and Ki67 expression in DLBCL patients treated with R-CHOP.

<p>Patients’ tumors were stained for (A, B) MYC, (C, D) BCL2, (E, F) BCL6, and (G, H) Ki67. The numbers of patients showing negative or positive stainings (MYC≥40%, BCL2≥70%, BCL6≥50%, Ki67≥90%), cut-off values, and <i>P</i> values are indicated.</p