  Based on first-principles calculations and full iterative solution of the
linearized Boltzmann-Peierls transport equation for phonons within three-phonon
scattering framework, we characterize the lattice thermal conductivities
$\kappa$ of strained and unstrained graphene. We find $\kappa$ converges to
5450 W/m-K for infinite unstrained graphene, while $\kappa$ diverges for
strained graphene with increasing system size at room temperature. The
different $\kappa$ behaviors for these systems are further validated
mathematically through phonon lifetime analysis. Flexural acoustic phonons are
the dominant heat carriers in both unstrained and strained graphene within the
temperature considered. Ultralong mean free paths of flexural phonons
contribute to finite size effects on $\kappa$ for samples as large as 8 cm at
room temperature. The calculated size-dependent and temperature-dependent
$\kappa$ for finite samples agree well with experimental data, demonstrating
the ability of the present approach to predict $\kappa$ of larger graphene
sample. Tensile strain hardens the flexural modes and increases their
lifetimes, causing interesting dependence of $\kappa$ on sample size and strain
due to the competition between boundary scattering and intrinsic phonon-phonon
scattering. These findings shed light on the nature of thermal transport in
two-dimensional materials and may guide predicting and engineering $\kappa$ of
graphene by varying strain and size.
