1. Some recent discoveries about half-arc-transitive graphs : dedicated to Dragan Marušič on the occasion of his 60th birthdayMarston D. E. Conder, Primož Potočnik, Primož Šparl, 2015, izvirni znanstveni članek Opis: We present some new discoveries about graphs that are half-arc-transitive (that is, vertex- and edge-transitive but not arc-transitive). These include the recent discovery of the smallest half-arc-transitive 4-valent graph with vertex-stabiliser of order 4, and the smallest with vertex-stabiliser of order 8, two new half-arc-transitive 4-valent graphs with dihedral vertex-stabiliser ▫$D_4$▫ (of order 8), and the first known half-arc-transitive 4-valent graph with vertex-stabiliser of order 16 that is neither abelian nor dihedral. We also use half-arc-transitive group actions to provide an answer to a recent question of Delorme about 2-arc-transitive digraphs that are not isomorphic to their reverse. Ključne besede: graph, edge-transitive, vertex-transitive, arc-transitive, half arc-transitive Objavljeno v RUP: 31.12.2021; Ogledov: 895; Prenosov: 16 Celotno besedilo (333,06 KB) |
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3. Edge elimination and weighted graph classesJesse Beisegel, Nina Chiarelli, Ekkehard Köhler, Matjaž Krnc, Martin Milanič, Nevena Pivač, Robert Scheffler, Martin Strehler, 2020, objavljeni znanstveni prispevek na konferenci Ključne besede: edge elimination, weighted graph, split graph, threshold graph, chain graph, linear-time recognition algorithm Objavljeno v RUP: 10.11.2020; Ogledov: 1506; Prenosov: 34 Povezava na celotno besedilo |
4. Edge elimination schemes of weighted graph classes, Workshop on Graph Modification algorithms, experiments and new problems, 23rd - 24th January 2020, Bergen, NorwayMartin Milanič, Jesse Beisegel, Nina Chiarelli, Ekkehard Köhler, Matjaž Krnc, Nevena Pivač, Robert Scheffler, Martin Strehler, 2020, vabljeno predavanje na konferenci brez natisa Ključne besede: graph class, edge elimination scheme, sandwich monotonicity Objavljeno v RUP: 28.05.2020; Ogledov: 1537; Prenosov: 0 |
5. Avoidable vertices and edges in graphsJesse Beisegel, Maria Chudnovsky, Vladimir Gurvich, Martin Milanič, Mary Agnes Milanič, 2019, objavljeni znanstveni prispevek na konferenci Ključne besede: simplicial vertex, avoidable vertex, avoidable edge, avoidable path, maximum weight clique problem, polynomial-time algorithm, hole-cyclically orientable graph Objavljeno v RUP: 20.08.2019; Ogledov: 2143; Prenosov: 156 Povezava na celotno besedilo |
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9. On two extensions of equimatchable graphsZakir Deniz, Tinaz Ekim, Tatiana Romina Hartinger, Martin Milanič, Mordechai Shalom, 2017, izvirni znanstveni članek Ključne besede: minimum maximal matching, equimatchable graph, edge dominating set, Gallai-Edmonds decomposition, parameterized complexity Objavljeno v RUP: 29.01.2018; Ogledov: 2344; Prenosov: 146 Povezava na celotno besedilo |
10. On cyclic edge-connectivity of fullerenesKlavdija Kutnar, Dragan Marušič, 2008, izvirni znanstveni članek Opis: A graph is said to be cyclically ▫$k$▫-edge-connected, if at least ▫$k$▫ edges must be removed to disconnect it into two components, each containing a cycle. Such a set of ▫$k$▫ edges is called a cyclic-k-edge cutset and it is called a trivial cyclic-k-edge cutset if at least one of the resulting two components induces a single ▫$k$▫-cycle. It is known that fullerenes, that is, 3-connected cubic planar graphs all of whose faces are pentagons and hexagons, are cyclically 5-edge-connected. In this article it is shown that a fullerene ▫$F$▫ containing a nontrivial cyclic-5-edge cutset admits two antipodal pentacaps, that is, two antipodal pentagonal faces whose neighboring faces are also pentagonal. Moreover, it is shown that ▫$F$▫ has a Hamilton cycle, and as a consequence at least ▫$15 \cdot 2^{n/20-1/2}$▫ perfect matchings, where ▫$n$▫ is the order of ▫$F$▫. Ključne besede: graph, fullerene graph, cyclic edge-connectivity, hamilton cycle, perfect matching Objavljeno v RUP: 03.04.2017; Ogledov: 2248; Prenosov: 138 Povezava na celotno besedilo |