Terminal-Pairability in Complete Bipartite Graphs

We investigate the terminal-pairibility problem in the case when the base graph is a complete bipartite graph, and the demand graph is also bipartite with the same color classes. We improve the lower bound on maximum value of $\Delta(D)$ which still guarantees that the demand graph $D$ is terminal-pairable in this setting. We also prove a sharp theorem on the maximum number of edges such a demand graph can have.Comment: 8 pages, several typos correcte

On L(2,1)-labelings of some products of oriented cycles

We refine two results of Jiang, Shao and Vesel on the L(2,1)-labeling number λ of the Cartesian and the strong product of two oriented cycles. For the Cartesian product, we compute the exact value of λ(Cm−→□Cn−→) for m, n≥40; in the case of strong product, we either compute the exact value or establish a gap of size one for λ(Cm−→⊠Cn−→) for m, n≥48

Terminal-Pairability in Complete Bipartite Graph of Non-Bipartite Demands

We investigate the terminal-pairability problem in the case when the base graph is a complete bipartite graph, and the demand graph is a (not necessarily bipartite) multigraph on the same vertex set. In computer science, this problem is known as the edge-disjoint paths problem. We improve the lower bound on the maximum value of $\Delta(D)$ which still guarantees that the demand graph $D$ has a realization in $K_{n,n}$. We also solve the extremal problem on the number of edges, i.e., we determine the maximum number of edges which guarantees that a demand graph is realizable in $K_{n,n}$.Comment: 15 pages, draws from arXiv:1702.0431

The heterotrimeric G-protein complex modulates light sensitivity in arabidopsis thaliana seed germination

Release of dormancy and induction of seed germination are complex traits finely regulated by hormonal signals and environmental cues such as temperature and light. The Red (R):Far-Red (FR) phytochrome photoreceptors mediate light regulation of seed germination. We investigated the possible involvement of heterotrimeric G-protein complex in the phytochrome signaling pathways of Arabidopsis thaliana seed germination. Germination rates of null mutants of the alpha (Gα) and beta (Gβ) subunits of the G-protein (Atgpa1-4 and agb1-2, respectively) and the double mutant (agb1-2/gpa1-4) are lower than the wildtype (WT) under continuous or pulsed light. The Gα and Gβ subunits play a role in seed germination under hourly pulses of R lower than 0.1 μmol m -2 s -1 whereas the Gβ subunit plays a role in higher R fluences. The germination of double mutants of G-protein subunits with phyA-211 and phyB-9 suggests that AtGPA1 seems to act as a positive regulator of phyA and probably phyB signaling pathways, while the role of AGB1 is ambiguous. The imbibition of seeds at 4°C and 35°C alters the R and FR light responsiveness of WT and G-protein mutants to a similar magnitude. Thus, Gα and Gβ subunits of the heterotrimeric G-protein complex modulate light induction of seed germination by phytochromes and are dispensable for the control of dormancy by low and high temperatures prior to irradiation. We discuss the possible indirect role of the G-protein complex on the phytochrome-regulated germination through hormonal signaling pathways.Fil: Botto, Javier Francisco. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Parque Centenario. Instituto de Investigaciones Fisiológicas y Ecológicas Vinculadas a la Agricultura. Universidad de Buenos Aires. Facultad de Agronomía. Instituto de Investigaciones Fisiológicas y Ecológicas Vinculadas a la Agricultura; ArgentinaFil: Ibarra, Silvia Elizabeth. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Parque Centenario. Instituto de Investigaciones Fisiológicas y Ecológicas Vinculadas a la Agricultura. Universidad de Buenos Aires. Facultad de Agronomía. Instituto de Investigaciones Fisiológicas y Ecológicas Vinculadas a la Agricultura; ArgentinaFil: Jones, Alan M.. University of North Carolina; Estados Unido