Partial cubes and their [tau]-graphs

Klavžar, Sandi; Kovše, Matjaž

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Title:	Partial cubes and their [tau]-graphs
Authors:	ID Klavžar, Sandi (Author) ID Kovše, Matjaž (Author)
Files:	http://dx.doi.org/10.1016/j.ejc.2006.04.006
Language:	English
Work type:	Not categorized
Typology:	1.01 - Original Scientific Article
Organization:	FNM - Faculty of Natural Sciences and Mathematics
Abstract:	Za delno kocko $G$ ima $tau$ -graph $G^tau$ ekvivalenčne razrede Djokovic-Winklerjeve relacije kot vozlišča, pri čemer sta razreda $E$ in $F$ sosednja, če neki povezavi $e in E$ in $f in F$ inducirata konveksno pot $P_3$ . Dokazano je, da za vsak graf $G$ obstaja medianski graf $M$ , tako da velja $G = M^tau$ , da je $G^tau$ povezan natanko tedaj, ko je $G$ pragraf glede na kartezični produkt grafov in da je $tau$ -graf medianskega grafa $G$ brez $K_n$ natanko tedaj, ko $G$ ne vsebuje konveksnega $K_{1,n}$ .
Keywords:	matematika, teorija grafov, delne kocke, medianski grafi, kartezični produkt grafov, mathematics, graf theory, partial cubes, median graphs, Cartesian product graphs
Year of publishing:	2007
Number of pages:	str. 1037-1042
Numbering:	Vol. 28, no. 4
PID:	20.500.12556/DKUM-51588
UDC:	519.17
ISSN on article:	0195-6698
COBISS.SI-ID:	14252377
NUK URN:	URN:SI:UM:DK:WG7V1HOA
Publication date in DKUM:	10.07.2015
Views:	1017
Downloads:	33
Metadata:
Categories:	Misc.
:	KLAVŽAR, Sandi and KOVŠE, Matjaž, 2007, Partial cubes and their [tau]-graphs. European journal of combinatorics [online]. 2007. Vol. 28, no. 4, p. 1037–1042. [Accessed 28 March 2025]. Retrieved from: http://dx.doi.org/10.1016/j.ejc.2006.04.006 Copy citation

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Record is a part of a journal

Title:	European journal of combinatorics
Shortened title:	Eur. j. comb.
Publisher:	Academic Press
ISSN:	0195-6698
COBISS.SI-ID:	25427968

Secondary language

Language:	Unknown
Title:	Delne kocke in njihovi [tau]-grafi
Abstract:	The $tau$ -graph $G^tau$ of a partial cube $G$ has the equivalence classes of the Djokovic-Winkler relation as vertices, two classes $E$ and $F$ being adjacent if some edges $e in E$ and $f in F$ induce a convex $P_3$ . It is shown that for every graph $G$ there exists a median graph $M$ such that $G = M^tau$ , that $G^tau$ is connected if and only if $G$ is a Cartesian prime graph, and that for a median graph $G$ its $tau$ -graph is $K_n$ -free if and only if $G$ contains no convex $K_{1,n}$ .

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