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Heavy quarks (charm and beauty) are produced in hard-scattering processes andthe study of their production in proton--proton (pp) collisions is an importanttest for calculations based on perturbative Quantum Chromodynamics (pQCD).Heavy-flavor production as a function of charged-particle multiplicity providesinsight into the processes occurring at the partonic level and the interplaybetween the hard and soft particle production mechanisms in pp collisions.  In this contribution, measurements of open heavy-flavor production as afunction of multiplicity, via the study of the $\mathrm{D}$-mesonself-normalized yields in pp collisions at the center-of-mass energy of$\sqrt{s} = 13$ TeV is presented. The $\mathrm{D}$-meson self-normalized yieldis found to increase stronger than linearly with increasing charged-particlemultiplicity. The measurements are compared to theoretical model calculations,and with the results at $\sqrt{s} = 7$ TeV.

Measurement of $\mathrm{D}$-meson production as a function of  charged-particle multiplicity in proton--proton collisions at $\sqrt{s} = 13$  TeV with ALICE at the LHC