We show that if G is a connected graph of maximum degree at most 4, which is not C2,5, then the strong matching number of G is at least 1 9n(G). This bound is tight and the proof implies a polynomial time algorithm to find an induced matching of this size.

We determine the maximum number of edges that a claw-free graph can have, when its maximum degree and matching number are bounded. This is a famous problem that has been studied on general graphs, and for which there is a tight bound. The graphs achieving this bound contain in most cases an induced copy of K1,3, the claw, which motivates studying the question on claw-free graphs. Note that on g...

The significant increase in using reservoir simulation models poses significant challenges in the design and calibration of models. Moreover, conventional model calibration, history matching, is usually performed using a trial and error process of adjusting model parameters until a satisfactory match is obtained. In addition, history matching is an inverse problem, and hence it may have non-uni...

In this paper, motivated by a question posed H. de Alba and D. T. Hoang, we introduce strongly biconvex graphs as subclass of weakly chordal bipartite graphs. We give linear time algorithm to find an induced matching for such prove that indeed gives maximum matching. Applying algorithm, provide graph whose (monomial) edge ideal does not admit unique extremal Betti number. Using constructed grap...

A matching is maximal if no other matching contains it as a proper subset. Maximal matchings model phenomena across many disciplines, including applications within chemistry. In this paper, we study maximal matchings in an important class of chemical compounds: polyphenylenes. In particular, we determine the extremal polyphenylene chains in regards to the number of maximal matchings. We also de...

Say that an edge of a graph G dominates itself and every other edge adjacent to it. An edge dominating set of a graph G = (V,E) is a subset of edges E′ ⊆ E which dominates all edges of G. In particular, if every edge of G is dominated by exactly one edge of E′ then E′ is a dominating induced matching. It is known that not every graph admits a dominating induced matching, while the problem to de...