Title: | Hamilton‐connected {claw, net}‐free graphs, II |
Authors: | Xia, Liu Ryjáček, Zdeněk Vrána, Petr Xiong, Liming Yang, Xiaojing |
Citation: | XIA, L. RYJÁČEK, Z. VRÁNA, P. XIONG, L. YANG, X. Hamilton‐connected {claw, net}‐free graphs, II. Journal of Graph Theory, 2023, roč. 103, č. 1, s. 119-138. ISSN: 0364-9024 |
Issue Date: | 2023 |
Publisher: | Wiley |
Document type: | článek article |
URI: | 2-s2.0-85141985587 http://hdl.handle.net/11025/51878 |
ISSN: | 0364-9024 |
Keywords in different language: | claw‐free;closure;forbidden subgraph;Hamilton‐connected;net‐free |
Abstract in different language: | In the first one in this series of two papers, we have proved that every 3‐connected {K(1,3), N(1,3,3)}‐free graph is Hamilton‐connected. In this paper, we continue in this direction by proving that every 3‐connected {K(1,3), X}‐free graph, where X ∈ {N(1,1,5), N(2,2,3)}, is Hamilton‐connected (where N(i,j,k) is the graph obtained by attaching endvertices of three paths of lengths i, j, k to a triangle). This together with a previous result of other authors completes the characterization of forbidden induced generalized nets implying Hamilton-connectedness of a 3‐connected claw‐free graph. We also discuss remaining open cases in a full characterization of connected graphs X such that every 3‐connected {K(1,3), X}‐free graph is Hamilton‐connected. |
Rights: | Plný text je přístupný v rámci univerzity přihlášeným uživatelům. © Wiley Periodicals LLC. |
Appears in Collections: | Články / Articles (KMA) Články / Articles (NTIS) OBD |
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