Completely Independent Spanning Trees in Line Graphs

Completely independent spanning trees in a graph $G$ are spanning trees of $G$ such that for any two distinct vertices of $G$, the paths between them in the spanning trees are pairwise edge-disjoint and internally vertex-disjoint. In this paper, we present a tight lower bound on the maximum number of completely independent spanning trees in $L(G)$, where $L(G)$ denotes the line graph of a graph $G$. Based on a new characterization of a graph with $k$ completely independent spanning trees, we also show that for any complete graph $K_n$ of order $n \geq 4$, there are $\lfloor \frac{n+1}{2} \rfloor$ completely independent spanning trees in $L(K_n)$ where the number $\lfloor \frac{n+1}{2} \rfloor$ is optimal, such that $\lfloor \frac{n+1}{2} \rfloor$ completely independent spanning trees still exist in the graph obtained from $L(K_n)$ by deleting any vertex (respectively, any induced path of order at most $\frac{n}{2}$) for $n = 4$ or odd $n \geq 5$ (respectively, even $n \geq 6$). Concerning the connectivity and the number of completely independent spanning trees, we moreover show the following, where $\delta(G)$ denotes the minimum degree of $G$. $\$ $\bullet$ Every $2k$-connected line graph $L(G)$ has $k$ completely independent spanning trees if $G$ is not super edge-connected or $\delta(G) \geq 2k$. $\$ $\bullet$ Every $(4k-2)$-connected line graph $L(G)$ has $k$ completely independent spanning trees if $G$ is regular. $\$ $\bullet$ Every $(k^2+2k-1)$-connected line graph $L(G)$ with $\delta(G) \geq k+1$ has $k$ completely independent spanning trees.Comment: 20 pages with 5 figure

Mutants in orthophosphate-regulated cyclic phosphodiesterase showing rhythmic condiation in Neurospora

Mutants in orthophosphate-regulated cyclic phosphodiesterase showing rhythmic conidiation in Neurospor

A simple method to isolate mutants in repressible cyclic phosphodiesterase in Neurospora crassa

A simple method to isolate mutants in repressible cyclic phosphodiesterase in Neurospora crassa

An efficient isolation method for meiotic mutants causing meiotic nondisjunction or elevated recombination frequency in Neurospora crassa.

An efficient isolation method for meiotic mutants causing meiotic nondisjunction or elevated recombination frequency in Neurospora crassa

Assay method and localization of GTP binding proteins in N. crassa.

Assay method and localization of GTP binding proteins in N. crassa

Interannual variability in the baroclinic gyre structure of the western North Pacific from 1954-1974

In the western North Pacific from 0-35N 130-180E, the vertical and horizontal thermal structure of the baroclinic gyre systems in the region from 0-400 m depth has been mapped on a yearly basis from 1954-1974. From this measure of the baroclinic field of mass, the dynamic height (0/400 db) has been computed for each year, yielding geostrophic current indices of the major zonal currents...

Quasi-stationary banded structure in the mean zonal geostrophic current regimes of the western North Pacific

Two data sets are used to reveal the quasi-stationary nature of the banded current structure in the western North Pacific. The first consists of all hydrographic data taken in the region, archived at the Japanese Oceanographic Data Center (JODC)…