Exact planar Turán numbers are established for K1+(P2∪P3), a combined C3/Θ4 configuration, and the disjoint union of C3 and Θ4, with extremal graph characterizations.
Extremal spectral results of planar graphs without vertex-disjoint cycles
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Planar Tur\'{a}n numbers of three configurations
Exact planar Turán numbers are established for K1+(P2∪P3), a combined C3/Θ4 configuration, and the disjoint union of C3 and Θ4, with extremal graph characterizations.