TWOHAMG(1)

💖 TWOHAMG 💖

okay bestie, sit down, hydrate, because we're about to talk about twohamg — it's the manual page for twohamg version 2.9.3 and it is so much cooler than it sounds. graph theory girlies rise 🫶

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✨ SYNOPSIS ✨

twohamg [-sgvq] [-L#] [infile [outfile]]

yes it's short. yes it goes hard. no notes. 💅

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🌸 DESCRIPTION 🌸

Partition quartic graphs into two hamiltonian cycles.

...and then it just outputs the ones that can't be partitioned. iconic behaviour honestly, it's giving "I only speak up when something's wrong" main character energy 😭

That's it. That's the whole job. Split the graph into two hamiltonian cycles, and if that's impossible, bestie gets a write-out. no cap.

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🎀 OPTIONS 🎀

• -s — force output to sparse6 format ✨
• -g — force output to graph6 format ✨

ngl, if you give it neither -s nor -g, the output format is decided by the header, or — if there's no header at all — by the format of the first input graph. also see -S. 👀

🦋 and listen: the output file will have a header if and only if the input file does. if and only if!! it's matching energy, it's twin flames, it's literally mirrored.

• -p — read a cubic graph and use its prism. Vertex i of the input becomes vertices 2*i, 2*i+1 in the prism. lowkey a glow-up transformation fr fr ✨
• -x — test for decompositions using each 2-path 🌈
• -X — as -x but only output if two 2-paths are missed at some vertex. yes it's the louder sibling. it's the same but it only speaks up when two 2-paths get missed at some vertex 👑
• -y — test for decompositions using each non-triangular 3-path 🍓
• -t# — with -x and -X, consider only paths with center #. with -y, consider only paths starting at #. so basically # is the VIP of your path selection, iykyk 💅
• -Y — with -p, only consider paths whose central edge is vertical 📐
• -v — give a partition for those graphs which have one, and a message for those which don't. and with -x, it lists the exceptional 2-paths too. it's chatty! we love a talkative queen 💖
• -L# — limit to 1000*# iterations; write with message if timeout. and heads up: graphs that time out are written to the output. so if it runs out of patience, it still leaves a note. respectful, honestly. 😭
• -q — suppress auxiliary information. for when you want the ✨bare minimum✨ and no side commentary. (rude but valid.)

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💀 quick vibe check: -x, -X, -y, -t#, and -Y all interact with each other, so read the little bullet notes before you mash flags together. fr fr. don't just yeet them in there.

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twohamg 2.9.3 · September 2026 — mwah, that's the whole page bestie, go partition some quartic graphs and slay 💅✨🦋💖