The　two-coloring　number　of　graphs,　which　was　originally　introduced　in　the　study　of　the　game　chromatic　number,　also　gives　an　upper　bound　on　the　degenerate　chromatic　number　as　introduced　by　Borodin.　It　is　proved　that　the　two-coloring　number　of　any　planar　graph　is　at　most　nine.　As　a　consequence,　the　degenerate　list　chromatic　number　of　any　planar　graph　is　at　most　nine.　It　is　also　shown　that　the　degenerate　diagonal　chromatic　number　is　at　most　11　and　the　degenerate　diagonal　list　chromatic　number　is　at　most　12　for　all　planar　graphs.