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- W1746286871 abstract "In this work we introduce the class of graphs with bounded induced distance of order k , (BID( k ) for short). A graph G belongs to BID( k ) if the distance between any two nodes in every connected induced subgraph of G is at most k times their distance in G . These graphs can model communication networks in which node failures may occur: at a given time, if sender and receiver are still connected, any message can be delivered through a path (that, due to node failures, could be longer than the shortest one) the length of which is at most k times the best possible. In this work we first provide two characterizations of graphs belonging to BID( k ): one based on the stretch number (a new invariant introduced here), and the other based on cycle-chord conditions. After that, we investigate classes with order k ⩽2. In this context, we note that the class BID(1) is the well known class of distance-hereditary graphs, and we show that 3/2 is a lower bound for the order k of graphs that are not distance-hereditary. Then, we characterize graphs in BID(3/2) by means of forbidden induced subgraphs, and we also show that graphs in BID(2) have a more complex characterization. We prove that the recognition problem for the generic class BID( k ) is Co-NP-complete. Finally, we show that the split composition can be used to generate graphs in BID( k )." @default.
- W1746286871 created "2016-06-24" @default.
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- W1746286871 date "2001-02-01" @default.
- W1746286871 modified "2023-09-29" @default.
- W1746286871 title "Graphs with bounded induced distance" @default.
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- W1746286871 doi "https://doi.org/10.1016/s0166-218x(00)00227-4" @default.
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