Kholmov tied for the title in the 2000 World Senior Championship at Rowy, on 8/11 with Mark Taimanov, Jānis Klovāns, and Alexander Chernikov.
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Kholmov got just one chance to represent the USSR in a team event at full international level when he played board ten at the European Team Championships, Kapfenberg 1970.
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At Voskresensk 1990, Kholmov tied 3rd–6th on 6.5/11 behind winners Igor Naumkin and Valery Neverov.