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1.
HAMILTONSKA DOPOLNITEV GRAFA
Nataša Brodnjak, 2011, undergraduate thesis

Abstract: Diplomsko delo obravnava hamiltonsko dopolnitev grafa. Število hamiltonske dopolnitve grafa G je najmanjše število povezav, ki jih moramo dodati grafu, da ta postane hamiltonski graf. V prvem poglavju predstavimo osnovne definicije iz teorije grafov in algoritmov, ki jih potrebujemo v nadaljevanju. Nato definiramo problem hamiltonske dopolnitve grafa ter soroden problem pokrivanja vozlišč s potmi. V tretjem poglavju predstavimo algoritma za hamiltonsko dopolnitev dreves. V četrtem poglavju opišemo reševanje hamiltonske dopolnitve grafa za poljuben graf. Na koncu diplomskega dela opišemo sorodne probleme.
Keywords: hamiltonski graf, hamiltonska dopolnitev grafa, pokrivanje s potmi, dodeljevanje frekvenc
Published: 07.07.2011; Views: 1267; Downloads: 75
.pdf Full text (486,63 KB)

2.
PERMUTAEDER
Klara Prah, 2011, undergraduate thesis

Abstract: V diplomskem delu bomo podrobneje obravnavali konveksni politop imenovan permutaeder. V prvem poglavju bomo spoznali matematične definicije nekaterih pojmov, ki jih bomo potrebovali v nadaljevanju. V drugem poglavju si bomo pogledali dokaz, da je graf permutaedra hamiltonski graf. V tretjem poglavju bomo dokazali, da razdalje med oglišči v n-dimenzionalnem permutaedru zavzemajo vsa soda števila. V četrtem poglavju si bomo pogledali asociaeder, ki posplošuje permutaeder.
Keywords: permutaeder, zonotop, konveksni politop, hamiltonski graf, minkowskyjeva vsota, Caylejev graf, asociaeder.
Published: 26.09.2011; Views: 1482; Downloads: 76
.pdf Full text (891,37 KB)

3.
On connectedness and hamiltonicity of direct graph bundles
Irena Hrastnik Ladinek, Janez Žerovnik, 2012, original scientific article

Abstract: A necessary and sufficient condition for connectedness of direct graph bundles where the fibers are cycles is given. It is also proved that all connected direct graph bundles ▫$X=C_stimes^{alpha}C_t$▫ are Hamiltonian.
Keywords: direktni produkt grafov, direktni grafovski sveženj, hamiltonski graf, povezan graf, direct graph product, direct graph bundle, Hamiltonian graph, connected graph, reflection, cyclic ▫$ell$▫-shift
Published: 10.07.2015; Views: 337; Downloads: 20
URL Link to full text

4.
Cyclic bundle Hamiltonicity
Irena Hrastnik Ladinek, Janez Žerovnik, 2011

Abstract: Cyclic bundle Hamiltonicity ▫$cbH(G)$▫ of a graph ▫$G$▫ is the minimal ▫$n$▫ for which there is an automorphism ▫$alpha$▫ of ▫$G$▫ such that the graph bundle ▫$C_nBox^{alpha} G$▫ is Hamiltonian. We define ▫$nabla (tilde{G}_{alpha})_{min}$▫, an invariant that is related to the maximal vertex degree of spanning trees suitably involving the symmetries of ▫$G$▫ and prove ▫$cbH(G) leq nabla(tilde{G}_{alpha})_{min} leq cbH(G)+1$▫ for any non-trivial connected graph ▫$G$▫.
Keywords: kartezični produkt, kartezični grafovski sveženj, hamiltonski graf, Cartesian product, Cartesian graph bundle, Hamiltonian graph
Published: 10.07.2015; Views: 467; Downloads: 58
URL Link to full text

5.
On connectivity and hamiltonicity of direct graph bundles
Irena Hrastnik Ladinek, Janez Žerovnik, 2011

Abstract: A necessary and sufficient condition for connectedness of direct graph bundles where the fibers are cycles is given. It is also proved that all connected direct graph bundles ▫$X=C_stimes^{alpha}C_t$▫ are Hamiltonian.
Keywords: direktni produkt grafov, direktni grafovski sveženj, hamiltonski graf, povezan graf, direct graph product, Cartesian graph bundle, Hamiltonian graph, connected graph, reflection, cyclic ▫$ell$▫-shift
Published: 10.07.2015; Views: 278; Downloads: 11
URL Link to full text

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