In a graph, a matching cut is an edge cut that is a matching. Matching Cut is the problem of deciding whether or not a given graph has a matching cut, which is known to be $${\mathsf {NP}}$$ NP -complete. While Matching Cut is trivial for graphs with minimum degree at most one, it is $${\mathsf {NP}}$$ NP -complete on graphs with minimum degree two. In this paper, we show that, for any given constant $$c>1$$ c > 1 , Matching Cut is $${\mathsf {NP}}$$ NP -complete in the class of graphs with minimum degree c and this restriction of Matching Cut has no subexponential-time algorithm in the number of vertices unless the Exponential-Time Hypothesis fails. We also show that, for any given constant $$\epsilon >0$$ ϵ > 0 , Matching Cut remains $${\mathsf {NP}}$$ NP -complete in the class of n-vertex (bipartite) graphs with unbounded minimum degree $$\delta >n^{1-\epsilon }$$ δ > n 1 - ϵ . We give an exact branching algorithm to solve Matching Cut for graphs with minimum degree $$\delta \ge 3$$ δ ≥ 3 in $$O^*(\lambda ^n)$$ O ∗ ( λ n ) time, where $$\lambda$$ λ is the positive root of the polynomial $$x^{\delta +1}-x^{\delta }-1$$ x δ + 1 - x δ - 1 . Despite the hardness results, this is a very fast exact exponential-time algorithm for Matching Cut on graphs with large minimum degree; for instance, the running time is $$O^*(1.0099^n)$$ O ∗ ( 1 . 0099 n ) on graphs with minimum degree $$\delta \ge 469$$ δ ≥ 469 . Complementing our hardness results, we show that, for any two fixed constants $$1< c <4$$ 1 < c < 4 and $$c^{\prime }\ge 0$$ c ′ ≥ 0 , Matching Cut is solvable in polynomial time for graphs with large minimum degree $$\delta \ge \frac{1}{c}n-c^{\prime }$$ δ ≥ 1 c n - c ′ .

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Literature reviews on performance measurement systems propose that firms should focus more on non-financial performance measures in addition to financial measures. This research will empirically investigate whether some contingency factors motivate the firms to use the integrated performance measures in order to improve their performance. The collected data of 257 Vietnamese manufacturing enterprises relating to the extent to which these firms use the integrated performance measures and their determinants as well as consequences was used to analyze through quantitative research methods under PLS_SEM analysis technique. The research results show that two contingency factors comprising differentiation strategy and the managerial accountants' participation in the strategic decision-making process have significantly positive effects on the use of the integrated performance measures. In addition, the use of the integrated performance measures plays a partly mediating role in the relationship between each of the contingency factors and organizational performance. Finally, the study also concludes that level of competition does not moderate the relationship between the use of the integrated performance measures and organizational performance whereas the managerial accountants' participation also does not play that role in the association between differentiation strategy and the use of the integrated performance measures. Therefore, in order to improve performance in the enterprises pursuing a higher differentiation strategy and much participation of managerial accountants in the strategic decision-making process, their managers need to apply more integrated performance measures.

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