Planar critical graphs

I'm giving a talk at the Korean Math Society's Spring meeting in Dae-jeon. I'm talking about a result with Eunkyong, Boram, and Ilkyoo on (5,2)-critical graphs.

They are all in the audience, except Ilkyoo because he can't wake up for a 9:20 talk. But for a joke, I say, "... this is joint work with Eunkyong Cho, Ilkyoo Choi and Boram Park, none of them are here today, so don't look for them. "

Boram smirks. Eunkyong looks confused and waves from her seat.

"No." I insist. "None of them are here. They had better things to do. I think Boram went to the dynamics session."

"They're here," someone says.

"No. They couldn't make it. There was a death in their families. It's tragic. Fishing accident."

Everyone looks around.

"They got Covid."

Frowns.

"Don't look for them. They aren't here." I insist. "How can I talk about graphs if nobody here trusts me? Math is about trust, and you lot got none of it in you."

"I trust you!" yells out Sang-june Lee.

"Thank you Sang-june!" I respond, "Everyone would do well to be more like Sang-june. He knows what side his bread is buttered on."

"The trust side!" he yells.

"Are you going to start your talk?" asks the session chair, "You only have 15 minutes."

"Fifteen minutes from when? My co-authors aren't even here yet."

"You've already used up 5 minutes." he says.

"Are you counting the time when you were talking?" I ask, "I don't see how that should count."

"It doesn't count!" yells out Sang-june. "Wait till his co-authors get here!"

"That's not how it works," says the chair. "We have other talks to get to."

"We are here." says Boram, seeming tired of the joke.

"No you're not!" yells Sang-june. "You missed your train!"

"That's okay Sang-june, the joke is ruined." I look angrily from the chair to Boram and back to the chair. "We are never going get the numbers that applied math gets if you guys can't take a little joke."

They look sufficiently contrite, and I start my talk. It was a little shorter than 15 minutes, but I've handled that deficiency very nicely.