Edge-Stable Equimatchable Graphs

A graph $G$ is \emph{equimatchable} if every maximal matching of $G$ has the same cardinality. We are interested in equimatchable graphs such that the removal of any edge from the graph preserves the equimatchability. We call an equimatchable graph $G$ \emph{edge-stable} if $G\setminus {e}$, that is the graph obtained by the removal of edge $e$ from $G$, is also equimatchable for any $e \in E(G)$. After noticing that edge-stable equimatchable graphs are either 2-connected factor-critical or bipartite, we characterize edge-stable equimatchable graphs. This characterization yields an $O(\min(n^{3.376}, n^{1.5}m))$ time recognition algorithm. Lastly, we introduce and shortly discuss the related notions of edge-critical, vertex-stable and vertex-critical equimatchable graphs. In particular, we emphasize the links between our work and the well-studied notion of shedding vertices, and point out some open questions

On contact graphs of paths on a grid

In this paper we consider Contact graphs of Paths on a Grid (CPG graphs), i.e. graphs for which there exists a family of interiorly disjoint paths on a grid in one-to-one correspondence with their vertex set such that two vertices are adjacent if and only if the corresponding paths touch at a grid-point. Our class generalizes the well studied class of VCPG graphs (see [1]). We examine CPG graphs from a structural point of view which leads to constant upper bounds on the clique number and the chromatic number. Moreover, we investigate the recognition and 3-colorability problems for B0- CPG, a subclass of CPG. We further show that CPG graphs are not necessarily planar and not all planar graphs are CPG

On Split B1-EPG Graphs

We consider the following problem: can a certain graph parameter of some given graph G be reduced by at least d, for some integer d, via at most k graph operations from some specified set S, for some given integer k? As graph parameters we take the chromatic number and the clique number. We let the set S consist of either an edge contraction or a vertex deletion. As all these problems are NP-complete for general graphs even if d is fixed, we restrict the input graph G to some special graph class. We continue a line of research that considers these problems for subclasses of perfect graphs, but our main results are full classifications, from a computational complexity point of view, for graph classes characterized by forbidding a single induced connected subgraph H

Bounding the chromatic number of squares of K-4-minor-free graphs

Deniz, Zakir/0000-0002-0701-0397WOS: 000471088300003Let G be a K-4-minor-free graph with Delta(G) >= 3. We prove that if G contains no subgraph isomorphic to K-2(,r) for some r >= 1. then chi(G(2)) <= Delta(G) + r. (C) 2019 Elsevier B.V. All rights reserved.TUBITAK-BIDEB, 2211 Ph.D. scholarship programmeWe thank anonymous referees for carefully reading our manuscript and for their invaluable comments and suggestions which substantially instigated many improvements on the readability of the material. The second and last authors are supported by TUBITAK-BIDEB, 2211 Ph.D. scholarship programme

Immobilization Of Laccase Onto A Porous Nanocomposite: Application For Textile Dye Degradation

Poly(MA-alt-MVE)-g-PLA/ODA-MMT nanocomposite was prepared by self-catalytic interlamellar graft copolymerization of L-lactic acid (LA) onto poly(maleic anhydride-alt-methyl vinyl ether) copolymer in the presence of octadecyl amine-montmorillonite (ODA-MMT) organoclay. FTIR, H-1 (C-13) NMR, XRD, and SEM-TEM were utilized for characterizing the resultant nanocomposite. Lactase from Trametes versicolor was immobilized onto the prepared nanocomposite by adsorption or covalent coupling. Decolorization of Reactive Red 3 from aqueous solution by laccase immobilized on the nanocomposite was studied in different conditions (pH, temperature, dye concentration, and reaction time) to investigate the decolorization activity with repeated use and storage. The results indicated that more than 77% of the activity of laccase immobilized systems was retained at the end of 10 cycles. The final decolorization capacity of the immobilized laccase was significantly higher (65%) than that of free laccase (33%) in the chosen optimized conditions (pH 5, 20 degrees C, 0.05 mg/mL laccase concentration, and 90 min).WoSScopu