"If there are no lips, the teeth will be cold." That was the phrase used by Chairman Mao to justify China's involvement in the Korean War against American-led forces in 1950.
And to a certain extent it has informed China's thinking ever since.
If North Korea - the lips in the metaphor - did not exist, the chances are that the peninsula would unite under the South's leadership.
For China - the teeth - this would mean sharing a border with a loyal and democratic US ally, and possibly even having to tolerate the presence of US troops in its backyard.
Worse still, the creation of a unified Korea might stir up secessionist sentiment among the millions of ethnic Koreans who live in China's north-east.
But are these fears enough to warrant propping up an increasingly bellicose and erratic regime?
From internet chat rooms to academic journals, many in China are increasingly saying no.
"This is part of the reason why China provides North Korea with presumably large amounts of aid as well as diplomatic cover at the United Nations," Shen Dingli, the vice president of the Institute of International Affairs at Fudan University, wrote in Foreign Policy magazine in February.
"And what thanks does China get in return? Lies, insults, and provocations.
"The loss of this 'ally' would be little felt in Beijing."
Others put it more succinctly. "Lips go to Hell!," wrote one user on China's popular micro-blogging site Weibo after North Korea carried out its third underground nuclear test on February 12. The same user added: "We should feel guilty that we ever danced with these guys."
This unusually harsh criticism represents a new source of pressure on China's leaders, who are also aware that how they deal with North Korea reflects on them both domestically and internationally.
In addition, the stakes have been raised by US plans to strengthen its missile defence system by adding equipment that it says is designed to protect against a North Korean attack, but that China believes could be effective against Chinese missiles too.
Some US officials and analysts say they already see signs of a change in China's stance towards its north-eastern neighbour.
Beijing has backed UN sanctions against North Korea and has not protested publicly about recent displays of US military force in South Korea, which included flying strategic stealth bombers over from the US.
Last weekend, China's new leader, Xi Jinping, delivered what some saw as a veiled warning to North Korea in a speech to a business conference in southern China.
"No nation should be allowed to throw the region or even the whole world into chaos for selfish gain," he said.
His comments came the day after China's foreign minister, Wang Yi, told the UN secretary general, Ban Ki-moon, that his county would "not allow troublemaking on its doorstep" during a discussion about the Korean peninsula.
The question among many analysts, however, is whether China is willing to go further than such carefully worded statements - a question that could equally apply to the US.
And even if China was willing to do more, how much influence does it really have over the new North Korean leader, Kim Jong-un?
"Kim Jong-un doen't listen to anybody, not to mention China," said Zhang Liangui, an expert on North Korea at the Central Party School, a Communist Party think tank and training college. "The West overestimates China's power because it doesn't know how North Korea regards China."
China's official position is that it opposes the nuclearisation of the Korean peninsula, and supports negotiations on North Korea's nuclear weapons programme through six-party talks involving Seoul, Pyongyang, Beijing, Moscow, Tokyo and Washington.
Since North Korea withdrew from those talks after a nuclear test in 2009, China's strategy has been to invest heavily in building infrastructure and promoting trade in border areas, in the hope of encouraging market reforms in North Korea.
Despite China's support for North Korea - as its biggest investor, trade partner and aid donor - North Korea paid no heed to Beijing's public warnings not to conduct its latest nuclear test.
"Kim Jong-un's childish tantrums have genuinely enraged China," said Zhu Feng, an international-relations expert at Peking University.
The problem, according to many Chinese analysts, is that China's military feels more than ever that it needs North Korea as a buffer against US forces because of the Obama administration's strategic "pivot" towards Asia.
"If China's surrounding area was stable and peaceful, it could afford to lose the DPRK, but the US's strategic shift makes China nervous," said Cheng Xiaohe, a North Korea expert at Renmin University in Beijing. "Against such a backdrop, China feels it needs friends."
That continuing strategic imperative helps to explain why Chinese authorities appear to have imposed a limit on the public debate about North Korea.
When Deng Yuwen, an editor at a Communist Party newspaper, overstepped the mark and called for Beijing to consider "abandoning" Pyongyang in an article published in the Financial Times, he was suspended from his job.
[ foreign.desk@thenational.ae ]
twitter: For breaking news from the Gulf, the Middle East and around the globe follow The National World. Follow us
