• Journal of applied mathematics & informatics
• /
• v.25 no.1_2
• /
• pp.339-344
• /
• 2007

The relationships between binding number and fractional edge (vertex)-deletability or fractional k-extendability of graphs are studied. Furthermore, we show that the result about fractional vertex-deletability are best possible.

• Journal of applied mathematics & informatics
• /
• v.25 no.1_2
• /
• pp.283-291
• /
• 2007

A simple graph G is said to be fractional n-factor-critical if after deleting any n vertices the remaining subgraph still has a fractional perfect matching. For fractional n-factor-criticality, in this paper, one necessary and sufficient condition, and three sufficient conditions related to maximum matching, complete closure are given.

• The Journal of Korean Institute of Electromagnetic Engineering and Science
• /
• v.19 no.8
• /
• pp.862-877
• /
• 2008

In this paper, two types of wideband 3-dB ring hybrids are compared and discussed to show the ring hybrid with a set of coupled-line sections better. However, the better one still has a realization problem that perfect matching can be achieved only with -3 dB coupling power. To solve the problem, a set of coupled-line sections with two shorts is synthesized using one- and two-port equivalent circuits and design equations are derived to have perfect matching, regardless of the coupling power. Based on the design equations, a modified ${\Pi}-type$ of transmission-line equivalent circuit is newly suggested. It consists of coupled-line sections with two shorts and two open stubs and can be used to reduce a transmission-line section, especially when its electrical length is greater than ${\pi}$. Therefore, the $3\;{\lambda}/4$ transmission-line section of a conventional ring hybrid can be reduced to less than ${\pi}/2$. To verify the modified ${\Pi}-type$ of transmission- line equivalent circuit, two kinds of simulations are carried out; one is fixing the electrical length of the coupled-line sections and the other fixing its coupling coefficient. The simulation results show that the bandwidths of resulting small transmission lines are strongly dependent on the coupling power. Using modified and conventional ${\Pi}-types$ of transmission-line equivalent circuits, a small ring hybrid is built and named a compact wideband coupled-line ring hybrid, due to the fact that a set of coupled-line sections is included. One of compact ring hybrids is compared with a conventional ring hybrid and the compared results demonstrate that the bandwidth of a proposed compact ring hybrid is much wider, in spite of being more than three times smaller in size. To test the compact ring hybrids, a microstrip compact ring hybrid, whose total transmission-line length is $220^{\circ}$, is fabricated and measured. The measured power divisions($S_{21}$, $S_{41}$, $S_{23}$ and $S_{43}$) are -2.78 dB, -3.34 dB, -2.8 dB and -3.2 dB, respectively at a design center frequency of 2 GHz, matching and isolation less than -20 dB in more than 20 % fractional bandwidth.