On P_4-tidy graphs

We study the P_4-tidy graphs, a new class defined by Rusu [30] in order to illustrate the notion of P_4-domination in perfect graphs. This class strictly contains the P_4-extendible graphs and the P_4-lite graphs defined by Jamison & Olariu in [19] and [23] and we show that the P_4-tidy graphs and P_4-lite graphs are closely related. Note that the class of P_4-lite graphs is a class of brittle graphs strictly containing the P_4-sparse graphs defined by Hoang in [14]. McConnel & Spinrad [2] and independently Cournier & Habib [5] have shown that the modular decomposition tree of any graph is computable in linear time. For recognizing in linear time P_4-tidy graphs, we apply a method introduced by Giakoumakis in [9] and Giakoumakis & Fouquet in [6] using modular decomposition of graphs and we propose linear algorithms for optimization problems on such graphs, as clique number, stability number, chromatic number and scattering number. We show that the Hamiltonian Path Problem is linear for this class of graphs. Our study unifies and generalizes previous results of Jamison & Olariu ([18], [21], [22]), Hochstattler & Schindler[16], Jung [25] and Hochstattler & Tinhofer [15]

On P_4-tidy graphs

this paper, we define the P 4 -tidy graphs, a new class of graphs strictly containing the previous considered classes (excepted the class defined by Fouquet & Giakoumakis in [6]). We show that the modular decomposition tree T (G) of a graph

On P_4-tidy graphs

We study the P_4-tidy graphs, a new class defined by Rusu [30] in order to illustrate the notion of P_4-domination in perfect graphs. This class strictly contains the P_4-extendible graphs and the P_4-lite graphs defined by Jamison & Olariu in [19] and [23] and we show that the P_4-tidy graphs and P_4-lite graphs are closely related. Note that the class of P_4-lite graphs is a class of brittle graphs strictly containing the P_4-sparse graphs defined by Hoang in [14]. McConnel & Spinrad [2] and independently Cournier & Habib [5] have shown that the modular decomposition tree of any graph is computable in linear time. For recognizing in linear time P_4-tidy graphs, we apply a method introduced by Giakoumakis in [9] and Giakoumakis & Fouquet in [6] using modular decomposition of graphs and we propose linear algorithms for optimization problems on such graphs, as clique number, stability number, chromatic number and scattering number. We show that the Hamiltonian Path Problem is linear for this class of graphs. Our study unifies and generalizes previous results of Jamison & Olariu ([18], [21], [22]), Hochstattler & Schindler[16], Jung [25] and Hochstattler & Tinhofer [15]

On P4-Tidy Graphs

We study the P 4-tidy graphs, a new class defined by Rusu [30] in order to illustrate the notion of P 4-domination in perfect graphs. This class strictly contains the P 4-extendible graphs and the P 4-lite graphs defined by Jamison & Olariu in [19] and [23] and we show that the P 4-tidy graphs and P 4-lite graphs are closely related. Note that the class of P 4-lite graphs is a class of brittle graphs strictly containing the P 4-sparse graphs defined by Hoang in [14]. McConnel & Spinrad [2] and independently Cournier & Habib [5] have shown that the modular decomposition tree of any graph is computable in linear time. For recognizing in linear time P 4-tidy graphs, we apply a method introduced by Giakoumakis in [9] and Giakoumakis & Fouquet in [6] using modular decomposition of graphs and we propose linear algorithms for optimization problems on such graphs, as clique number, stability number, chromatic number and scattering number. We show that the Hamiltonian Path Problem is linear for this class of graphs. Our study unifies and generalizes previous results of Jamison & Olariu ([18], [21], [22]), Hochstattler & Schindler[16], Jung [25] and Hochstattler & Tinhofer [15]

Scattering number and modular decomposition

AbstractThe scattering number of a graph G equals max {c(G⧹S) − |S|S is a cutset of G} where c(G⧹S) denotes the number of connected components in G⧹S. Jung (1978) has given for any graph having no induced path on four vertices (P4-free graph) a correspondence between the value of its scattering number and the existence of Hamiltonian paths or Hamiltonian cycles. Hochstättler and Tinhofer (to appear) studied the Hamiltonicity of P4-sparse graphs introduced by Hoàng (1985).In this paper, using modular decomposition, we show that the results of Jung and Hochsta̋ttler and Tinhofer can be generalized to a subclass of the family of semi-P4-sparse graphs introduced in Fouquet and Giakoumakis (to appear)

Simulating the Effect of Torrefaction on the Heating Value of Barley Straw

Many recent studies focused on the research of thermal treated biomass in order to replace fossil fuels. These studies improved the knowledge about pretreated lignocellulosics contribution to achieve the goal of renewable energy sources, reducing CO2 emissions and limiting climate change. They participate in renewable energy production so that sustainable consumption and production patterns can by ensured by meeting Goals 7 and 12 of the 2030 Agenda for Sustainable Development. To this end, the subject of the present study relates to the enhancement of the thermal energy content of barley straw through torrefaction. At the same time, the impact of the torrefaction process parameters, i.e., time and temperature, was investigated and kinetic models were applied in order to fit the experimental data using the severity factor, R0, which combines the effect of the temperature and the time of the torrefaction process into a single reaction ordinate. According to the results presented herein, the maximum heating value was achieved at the most severe torrefaction conditions. Consequently, torrefied barley straw could be an alternative renewable energy source as a coal substitute or an activated carbon low cost substitute (with/without activation treatment) within the biorefinery and the circular economy concept