Question: When did the stalemate happen in the war where UN troops approached the Yalu River?

Knowledge 1: Yalu River
The Korean side of the river was heavily industrialized during the period of Japanese rule (1910 -- 1945), and by 1945 almost 20% of Imperial Japan's total industrial output originated in Korea. During the Korean War, the movement of United Nations troops approaching the river precipitated massive Chinese intervention from around Dandong. In the course of the conflict every bridge across the river except one was destroyed. The one remaining bridge was the Sino -- Korean Friendship Bridge connecting Sinuiju, North Korea to Dandong, China. During the war the valley surrounding the western end of the river also became the focal point of a series of dogfights for air superiority over North Korea, earning the nickname ``MiG Alley ''in reference to the MiG - 15 fighters flown by the combined North Korean, Chinese and Soviet forces. [SEP] Knowledge 2: Korean War
After these reversals of fortune, which saw Seoul change hands four times, the last two years of fighting became a war of attrition, with the front line close to the 38th parallel. The war in the air, however, was never a stalemate. North Korea was subject to a massive bombing campaign. Jet fighters confronted each other in air - to - air combat for the first time in history, and Soviet pilots covertly flew in defense of their communist allies.
Knowledge 1: Yalu River
The Korean side of the river was heavily industrialized during the period of Japanese rule (1910 -- 1945), and by 1945 almost 20% of Imperial Japan's total industrial output originated in Korea. During the Korean War, the movement of United Nations troops approaching the river precipitated massive Chinese intervention from around Dandong. In the course of the conflict every bridge across the river except one was destroyed. The one remaining bridge was the Sino -- Korean Friendship Bridge connecting Sinuiju, North Korea to Dandong, China. During the war the valley surrounding the western end of the river also became the focal point of a series of dogfights for air superiority over North Korea, earning the nickname ``MiG Alley ''in reference to the MiG - 15 fighters flown by the combined North Korean, Chinese and Soviet forces. [SEP] Knowledge 2: Korean War
The Chinese counterattacked in April 1951, with the Fifth Phase Offensive, also known as the Chinese Spring Offensive, with three field armies (approximately 700,000 men). The offensive's first thrust fell upon I Corps, which fiercely resisted in the Battle of the Imjin River (22–25 April 1951) and the Battle of Kapyong (22–25 April 1951), blunting the impetus of the offensive, which was halted at the "No-name Line" north of Seoul. On 15 May 1951, the Chinese commenced the second impulse of the Spring Offensive and attacked the ROK Army and the U.S. X Corps in the east at the Soyang River. After initial success, they were halted by 20 May. At month's end, the U.S. Eighth Army counterattacked and regained "Line Kansas", just north of the 38th parallel. The UN's "Line Kansas" halt and subsequent offensive action stand-down began the stalemate that lasted until the armistice of 1953.
Knowledge 1: Yalu River
The Korean side of the river was heavily industrialized during the period of Japanese rule (1910 -- 1945), and by 1945 almost 20% of Imperial Japan's total industrial output originated in Korea. During the Korean War, the movement of United Nations troops approaching the river precipitated massive Chinese intervention from around Dandong. In the course of the conflict every bridge across the river except one was destroyed. The one remaining bridge was the Sino -- Korean Friendship Bridge connecting Sinuiju, North Korea to Dandong, China. During the war the valley surrounding the western end of the river also became the focal point of a series of dogfights for air superiority over North Korea, earning the nickname ``MiG Alley ''in reference to the MiG - 15 fighters flown by the combined North Korean, Chinese and Soviet forces. [SEP] Knowledge 2: Korean War
For the remainder of the Korean War the UN Command and the PVA fought, but exchanged little territory; the stalemate held. Large - scale bombing of North Korea continued, and protracted armistice negotiations began 10 July 1951 at Kaesong. On the Chinese side, Zhou Enlai directed peace talks, and Li Kenong and Qiao Guanghua headed the negotiation team. Combat continued while the belligerents negotiated; the UN Command forces' goal was to recapture all of South Korea and to avoid losing territory. The PVA and the KPA attempted similar operations, and later effected military and psychological operations in order to test the UN Command's resolve to continue the war.

Answer: began 10 July 1951