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Which cubic graphs have quadrangulated spherical immersions?
Lowell Abrams, Yosef Berman, Vance Faber, Michael Murphy, 2026, izvirni znanstveni članek

Opis: We consider spherical quadrangulations – spherical embeddings of multigraphs, possibly with loops, so that every face has boundary walk of length 4 – in which all vertices have degree 3 or 4. Interpreting each degree 4 vertex as a crossing, these embeddings can also be thought of as transversal immersions of cubic graphs which we refer to as the extracted graphs. We also consider quadrangulations of the disk in which interior vertices have degree 3 or 4 and boundary vertices have degree 2 or 3. First, we classify all such quadrangulations of the disk. Then, we provide four methods for constructing spherical quadrangulations, two of which use quadrangulations of the disk as input. Two of these methods provide one-parameter families of quadrangulations, for which we prove that the sequence of isomorphism types of extracted graphs is periodic. We close with a description of computer computations which yielded spherical quadrangulations for all but three cubic multigraphs on eight vertices.
Ključne besede: spherical embedding, immersion, quadrangulation
Objavljeno v RUP: 17.03.2026; Ogledov: 734; Prenosov: 43
.pdf Celotno besedilo (1,05 MB)

3.
Upper embeddability of graphs and products of transpositions associated with edges
Shuhei Tsujie, Ryo Uchiumi, 2025, izvirni znanstveni članek

Opis: Given a graph, we associate each edge with the transposition which exchanges the endvertices. Fixing a linear order on the edge set, we obtain a permutation of the vertices. Dénes proved that the permutation is a full cyclic permutation for any linear order if and only if the graph is a tree. In this article, we characterize graphs having a linear order such that the associated permutation is a full cyclic permutation in terms of graph embeddings. Moreover, we give a counter example for Eden's question about an edge ordering whose associated permutation is the identity.
Ključne besede: full cyclic permutation ordering, upper-embeddable graph, 2-cell embedding, rotation system
Objavljeno v RUP: 21.10.2025; Ogledov: 877; Prenosov: 7
.pdf Celotno besedilo (324,31 KB)

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Bridging the question–answer gap in retrieval-augmented generation : hypothetical prompt embeddings
Domen Vake, Jernej Vičič, Aleksandar Tošić, 2025, izvirni znanstveni članek

Opis: Retrieval-Augmented Generation (RAG) systems synergize retrieval mechanisms with generative language models to enhance the accuracy and relevance of responses. However, bridging the style gap between user queries and relevant information in document text remains a persistent challenge in retrieval-augmented systems, often addressed by runtime solutions (e.g., Hypothetical Document Embeddings (HyDE)) that attempt to improve alignment but introduce extra computational overhead at query time. To address these challenges, we propose Hypothetical Prompt Embeddings (HyPE), a framework that shifts the generation of hypothetical content from query time to the indexing phase. By precomputing multiple hypothetical prompts for each data chunk and embedding the chunk in place of the prompt, HyPE transforms retrieval into a question-question matching task, bypassing the need for runtime synthetic answer generation. This approach does not introduce latency but also strengthens the alignment between queries and relevant context. Our experimental results on six common datasets show that HyPE can improve retrieval context precision by up to 42 percentage points and claim recall by up to 45 percentage points, compared to standard approaches, while remaining compatible with re-ranking, multi-vector retrieval, query decomposition, and other RAG advancements.
Ključne besede: LLM, hypothetical prompt embedding, Retrieval-Augmented Generation (RAG)
Objavljeno v RUP: 04.08.2025; Ogledov: 2038; Prenosov: 42
.pdf Celotno besedilo (1,41 MB)
Gradivo ima več datotek! Več...

6.
Classification of reflexible Cayley maps for dihedral groups
István Kovács, Young Soo Kwon, 2017, izvirni znanstveni članek

Ključne besede: Cayley map, regular embedding, reflexible map
Objavljeno v RUP: 02.03.2018; Ogledov: 4823; Prenosov: 135
URL Povezava na celotno besedilo

7.
Archimedean maps of higher genera
Ján Karabáš, Roman Nedela, 2012, izvirni znanstveni članek

Ključne besede: maps, graphs, embedding
Objavljeno v RUP: 03.04.2017; Ogledov: 4748; Prenosov: 182
URL Povezava na celotno besedilo

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Regular embeddings of cycles with multiple edges revisited
Kan Hu, Roman Nedela, Martin Škoviera, Naer Wang, 2015, izvirni znanstveni članek

Opis: Regularne vložitve ciklov z večkratnimi povezavami se pojavljajo v literaturi že kar nekaj časa, tako v topološki teoriji grafov kot tudi izven nje. Ta članek izriše kompletno podobo teh zemljevidov na ta način, da povsem opiše, klasificira in enumerira regularne vložitve ciklov z večkratnimi povezavami tako na orientabilnih kot tudi na neorientabilnih ploskvah. Večina rezultatov je sicer znana v tej ali oni obliki, toda tu so predstavljeni iz poenotenega zornega kota, osnovanega na teoriji končnih grup. Naš pristop daje dodatno informacijo tako o zemljevidih kot o njihovih grupah avtomorfizmov, priskrbi pa tudi dodaten vpogled v njihove odnose.
Ključne besede: regularna vložitev, večkratna povezava, Hölderjev izrek, Möbiusov zemljevid, regular embedding, multiple edge, Hölder's Theorem, Möbius map
Objavljeno v RUP: 15.10.2015; Ogledov: 6028; Prenosov: 115
URL Povezava na celotno besedilo

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