Yemen's third-largest city is being asphyxiated. The Houthis have captured the sole road linking Taiz to the southern port of Aden, cutting off humanitarian supplies to a city whose population exceeds 4 million. Prices for basic goods have multiplied. The World Food Programme reports 800,000 people severed from life-saving assistance, with 18 million Yemenis nationwide facing severe food insecurity. Between August 1 and October 19, at least 32 civilians — 14 of them children — were killed in fighting in Taiz governorate alone. UN Human Rights Chief Volker Turk issued a direct demand on Tuesday: the Houthis must immediately allow humanitarian aid into the city and permit civilians to leave freely. Yemen's internationally recognised government has appealed to the UN to intervene, and Presidential Leadership Council President Rashad al-Alimi formally requested the Houthis be designated a "terrorist organisation." The diplomatic escalation signals desperation — the government's military options are narrowing even as its rhetoric sharpens. The ground reality is grim. The government launched "Dawn of Yemen" on October 5 to reverse Houthi advances, and initial air strikes reportedly killed hundreds of Houthi fighters. But military analyst Ali al-Dahab told Al Jazeera the offensive has stalled: "The transition from defence to offence remains limited on the ground, and the map of the Yemeni government's influence in al-Marib has not expanded." He noted government forces must exploit gaps created by air strikes with multi-directional ground operations toward Sanaa — something they have not yet demonstrated the capacity to do. Meanwhile, the Houthis struck back hard. A ballistic missile attack on al-Alam military camp in Shabwa governorate killed 73, prompting the government to call it a "treacherous bloody assault" and a war crime. Cross-border exchanges between Houthis and Saudi Arabia have intensified, with the Saudi-led coalition intercepting a missile aimed at Riyadh and activating civil defense early warning systems across the capital. The Houthis are fighting on multiple fronts simultaneously — besieging Taiz, striking Saudi territory, and holding the Kahboub mountains in Lahij for their commanding view over the Gulf of Aden and the southern Red Sea. External involvement is expanding but constrained. The United Kingdom announced deployment of Typhoon fighter jets to defend Saudi Arabia, explicitly limiting the role to "defensive" operations with no strikes inside Yemen. Egypt's parliament delayed a vote to authorize military support for Saudi Arabia — a telling hesitation. Al-Dahab assessed the probability of international ground forces as "slim," with participation limited to air and naval support. This is the fundamental pattern: external actors are willing to provide firepower but not to absorb the casualties required to change facts on the ground. The siege of Taiz is not new — the city has been repeatedly besieged throughout the war — but its recurrence exposes the structural failure at the core of this conflict. No amount of aerial attrition breaks the Houthis' hold on terrain they are willing to defend with infantry. The government controls the sky and the sea approaches; the Houthis control the mountains and the roads. Civilians in Taiz pay the price for this stalemate in hunger, displacement, and death. The strategic picture is one of escalation without resolution. More jets, more missiles, more cross-border strikes — but no mechanism to end the siege, reopen supply routes, or protect the 4 million people trapped in a city that has become a recurring emblem of Yemen's decade-long catastrophe.