An i-triangulated graph is a graph in which every odd cycle has two non-crossing chords; i-triangulated graphs form a subfamily of perfect graphs. A slightly more general family of perfect graphs are clique-separable graphs. A graph is clique-separable precisely if every induced subgraph either has a clique cutset, or is a complete multipartite graph or a clique joined to an arbitrary bipartite...

We present a polynomial-time algorithm for recognizing quasi-Meyniel graphs. A hole is a chordless cycle with at least four vertices. A cap is a cycle with at least 6ve vertices, with a single chord that forms a triangle with two edges of the cycle. A graph G is quasi-Meyniel if it contains no odd hole and for some x ∈ V (G), the chord of every cap in G has x as an endvertex. Our recognition al...

For every integer k 2 and graph G; consider the following natural procedure: if G has a component G0 that is not k-connected, remove G0 if jG0j k, otherwise remove a cutset U V (G0) with jU j < k; do the same with the remaining graph until only k-connected components are left or all vertices are removed. We are interested when this procedure stops after removing o (jGj) vertices. Surprisingly, ...

A graph G is bridged if every cycle C of length at least 4 has vertices x; y such that dG(x; y )< dC (x ; y ). A cycle C is isometric if dG(x; y )1⁄4 dC (x; y ) for all x; y 2 V (C). We show that every graph contractible to a graph with girth g has an isometric cycle of length at least g. We use this to show that every minimal cutset S in a bridged graph G induces a connected subgraph. We intro...

Abstract Solving problems on graphs dynamically calls for algorithms to function under repeated modifications the graph and be more efficient than solving problem whole from scratch after each modification. Dynamic have been considered several properties, example connectivity, shortest paths recognition. In this paper we present fully dynamic recognition of threshold chain graphs, which are opt...

Let $t&gt;0$ be a real number and $G$ graph. We say is $t$-tough if for every cutset $S$ of $G$, the ratio $|S|$ to components $G-S$ at least $t$. Determining toughness an NP-hard problem arbitrary graphs. The Toughness Conjecture Chv\'atal, stating that there exists constant $t_0$ such $t_0$-tough graph with three vertices hamiltonian, still open in general. A called $(P_2\cup P_3)$-free it do...

| In this paper, a multi-way FPGA partitioning procedure FPART is introduced. The objective function of this procedure is to reduce the number of FPGA devices and the IOB utilization. An improved min-span FM bi-partitioning algorithm on the basis of an advanced gain model is adopted as the fundamental method, and three modules: init-part, optimize, and merge are combined in FPART to approach be...

In this paper we describe qualitative constraint-based modeling and reasoning strategies for simulationand diagnosis of continuous dynamic systems. We introduce a Qualitative Deviations Equations language for modeling the correct and faulty behavior of dynamic physical systems. We then address the task of implementing the language in a constraint processing framework, using heuristics (cycle cu...

The point we try to get across is that the generalization of the counterparts of the matroid theory in Cayley graphs since the matroid theory frequently simplify the graphs and so Cayley graphs. We will show that, for a Cayley graph ΓG, the cutset matroid M ∗(ΓG) is the dual of the circuit matroid M(ΓG). We will also deduce that if Γ ∗ G is an abstract-dual of a Cayley graph Γ, then M(Γ∗ G ) is...

Communication over a quantum broadcast channel with cooperation between the receivers is considered. The first form of addressed classical conferencing, where receiver 1 can send messages to 2. Another setting involves teleport state When not required recover information and its sole purpose help transmission 2, model reduces primitive relay channel. conferencing intimately related repeaters as...