Keilim18: 9
מִטָּה שֶׁנִּגְנַב חֶצְיָהּ, אוֹ אָבַד חֶצְיָהּ, אוֹ חֲלָקוּהָ אַחִין, אוֹ שֻׁתָּפִין — טְהוֹרָה. הֶחֱזִירוּהָ — מְקַבֶּלֶת טֻמְאָה מִכָּאן וּלְהַבָּא. מִטָּה מִטַּמְּאָה חֲבִילָה, וּמִטַּהֶרֶת חֲבִילָה, דִּבְרֵי רַבִּי אֱלִיעֶזֶר. וַחֲכָמִים אוֹמְרִים: מִטַּמְּאָה אֵבָרִים, וּמִטַּהֶרֶת אֵבָרִים.
A bed of which half was stolen, or half was lost, or which was divided by brothers, or [divided by] partners, is tahor. If they put it back together, it is susceptible to tumah from now on. [The components of] a bed can contract tumah as a unit, and [they] can be purified as a unit, [these are] the words of R’ Eliezer. But the Sages say: [They] can contract tumah [only as individual] parts, and can be purified [only as individual] parts.
Keilim19: 1
הַמְפָרֵק אֶת הַמִּטָּה לְהַטְבִּילָהּ, וְהַנּוֹגֵעַ בַּחֲבָלִין — טָהוֹר. הַחֶבֶל מֵאֵימָתַי הוא חִבּוּר לַמִּטָּה? מִשֶּׁיְּסָרֵג בָּהּ שְׁלשָׁה בָתִּים. וְהַנּוֹגֵעַ מִן הַקֶּשֶׁר וְלִפְנִים — טָמֵא; מִן הַקֶּשֶׁר וְלַחוּץ — טָהוֹר. נִימֵי הַקֶּשֶׁר, הַנּוֹגֵעַ בְּצָרְכּוֹ — טָמֵא. וְכַמָּה הוּא צָרְכּוֹ? רַבִּי יְהוּדָה אוֹמֵר: שָׁלשׁ אֶצְבָּעוֹת
One who disassembles a bed in order to immerse it, and one who touches its ropes, are tahor. At what point is the rope [considered] connected to the bed? From when three battim are woven into [the bed]. And one who touches [the rope] from the knot and inward is tamei. [If he touches the rope] from the knot and outward, [he is] tahor. [Regarding] the strands of the knot, one who touches the [part] necessary [for the knot] is tamei. And how much [of the strand] is necessary [for the knot]? R’ Yehudah says: Three fingerwidths.