It is well-known that every triangulation on a closed surface
F
2
has a spanning quadrangulation
Q
, and in particular,
Q
is bipartite if
F
2
is the sphere. In other words, every triangulation on the ...sphere has a polychromatic 2-coloring, which is a (not necessarily proper) 2-coloring of a graph on a closed surface without a monochromatic face. In this paper, we consider the balancedness of a polychromatic 2-coloring of graphs, that is, whether the difference in size of each color class is at most one. We verify that every 3-colorable triangulation has a balanced polychromatic 2-coloring. On the other hand, we construct an infinite family of triangulations
G
with order
n
on the sphere such that for every polychromatic 2-coloring of
G
, the size of color classes differs at least
n
3
-
2
. Then we conjecture that every triangulation on the sphere has a polychromatic 2-coloring whose size of color classes differs at most one-third of the number of vertices, and we give partial solutions for the conjecture.
In this paper, we prove that any two triangulations
G
and
G
′
on the sphere with exactly two odd degree vertices can be transformed into each other by two local transformations, called an
N
-
flip
...and a
P
2
-
flip
, preserving the parity of degree of each vertex, if
|
V
(
G
)
|
=
|
V
(
G
′
)
|
. This is an analogy of the same result for triangulations with each vertex even degree
7
, but we prove such a fact does not hold for triangulations with at least four odd degree vertices.
Recent experiments showed that the tunneling current through Si p/n junction is remarkably enhanced when isoelectronic impurity pairs such as Al+N are doped, which is promising for realizing Si ...tunneling field-effect transistors. To clarify the origin of such enhancement, the tunneling probability of electron carriers assisted by an Al+N isoelectronic trap (IET) in Si p/n junction was studied based on the perturbation theory using the results of first-principles calculations. We found that the enhancement is caused by two factors; (1) IET electronic state is located in the band gap of Si and works to decrease the tunneling length as a stepping stone. (2) Due to the localization feature of IET state, the electronic transition from valence bands to the IET state increases.
The ionization and diffusion of metal atoms at metal/SiO2 interfaces under an electric field are studied by first-principles calculation. It is shown that the ionization of metal atoms occurs when ...the hybridization of metal-atom electronic states with metal-induced gap states (MIGS) is broken. Moreover, we show that an electric field markedly decreases the penetration barrier of metal atoms from a metal electrode into SiO2 and enhances the diffusion of metal atoms.
3-dynamic coloring of planar triangulations Asayama, Yoshihiro; Kawasaki, Yuki; Kim, Seog-Jin ...
Discrete mathematics,
November 2018, 2018-11-00, Letnik:
341, Številka:
11
Journal Article
Recenzirano
Odprti dostop
An r-dynamic k-coloring of a graph G is a proper k-coloring such that any vertex v has at least min{r,degG(v)} distinct colors in NG(v). The r-dynamic chromatic numberχrd(G) of a graph G is the least ...k such that there exists an r-dynamic k-coloring of G.
Loeb et al. (2018) showed that if G is a planar graph, then χ3d(G)≤10, and there is a planar graph G with χ3d(G)=7. Thus, finding an optimal upper bound on χ3d(G) for a planar graph G is a natural interesting problem. In this paper, we show that χ3d(G)≤5 if G is a planar triangulation. The upper bound is sharp.
We define two reductions a 4-contradiction and a 2-removal for even triangulation on a surface. It is well known that these reductions preserve some properties of graphs. The complete lists of ...minimal even triangulations for the sphere, the projective plane and the torus with respect to these reductions have been already determined. In this paper, we make the complete list of minimal even triangulations of the Klein bottle and prove some applications by checking the list.
We clarify the physical origin of excellent performance and reliability in AgW-alloy ionic memory. AgW-alloy ionic memory shows low operation current in sub- \boldsymbol{\mu}\mathbf{A} range, good ...data retention and low operation voltage, which are desirable characteristics for high-density cross-point applications. Mechanisms of the improvements in AgW alloy devices compared to pure Ag and AgTi alloy devices are discussed based on first-principles calculations. We find that large cohesive energy of W is a key for improving data retention while keeping low operation voltage in AgW-alloy ionic memory.
